September 2022


How to Learn Matrix for JEE

As far as the JEE Main is concerned, Maths is an important subject. Once learned properly, students can easily score good marks in the JEE Maths exam. They should be thorough with all the formulas and theorems in Maths. Learning the formulas thoroughly will definitely help the students to save time during the exams. Maths is a subject which has a number of tricks to find the correct answer. Students should learn these tricks so that they can easily get the correct solutions. Byhearting the solutions will not work for Maths.

Let us discuss an easy and interesting topic in maths: matrix. When we arrange numbers in rows and columns, we call it a matrix. We can say that it is a rectangular array of numbers in rows and columns. Students can expect questions from matrices for any engineering entrance exam. Students are recommended to make use of each and every available resource to learn about the matrix. In this article, we will discuss matrix multiplication properties, types, addition properties, etc.

Matrix Multiplication – Properties

Following are the properties of matrix multiplication.

  • Not commutative
  • Associative
  • Distributive
  • Zero matrix multiplication
  • Multiplicative identity

Let M is a square matrix, and N be another square matrix. We can say that MN is not equal to NM. The commutative property does not satisfy here.

Matrix Addition – Properties

Following are the properties of matrix addition.

  • Commutative
  • Associative
  • Identity
  • Additive inverse

In matrix addition, the commutative property is satisfied.

Scalar Multiplication – Properties

Let M be a matrix, and N be another matrix of the same order, and p and q be two scalars, then:

  • p(M + N) = pM + pN
  • (p + q)M = pM + qM
  • p(qM) = (pqM) = q(pM)
  • (-pM) = -(pM) = p(-M)
  • tr(pM) = p tr(M), tr denotes trace of matrix.

Matrix – Types

The different types are given in the table below.

Row matrix Column matrix
Null matrix Singleton matrix
Diagonal matrix Scalar matrix
Horizontal matrix Vertical matrix
Square matrix Identity matrix
Triangular matrix Singular matrix
Non-singular matrix Symmetric matrix
Skew symmetric matrix Hermitian matrix
Skew-Hermitian matrix Idempotent matrix
Nilpotent matrix Periodic matrix
Involutary matrix Transpose matrix


Let A be a square matrix of order two having elements a11, a12, a21, a22. To calculate the determinant, we multiply a11 and a22. Then, multiply a21 and a12. Then, find the difference (a11a22 – a21a12). Students can expect questions from determinants for the JEE Main and the JEE Advanced. The determinant is an easy topic if learned properly. Students can easily score full marks on this topic if they learn the important formulas and properties. They are recommended to practice as many previous years’ questions as possible. It will help to improve their speed.

Time management is an important factor which determines the rank of the student in any entrance exam. Solving previous year’s questions and mock tests will help students to complete the exam within the stipulated time. Visit BYJU’S to download and learn previous years’ question papers, important formula PDFs, chapter-wise questions etc.

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Get Your Own Custom-Fit Sports Earbuds from Bose

If you’re looking for a way to take your workouts to the next level, you need to check out custom-fit sports earbuds from Bose. These earbuds are designed to fit snugly and comfortably in your ear, no matter what kind of activity you’re doing. So whether running, biking, or lifting weights, these earbuds will stay in place and give you the ultimate listening experience.

Custom-fit sports earbuds from Bose are also sweating and weather-resistant, so you don’t have to worry about them slipping out or getting damaged while you’re sweating. Plus, they come with various tips and ear tips to ensure you get the perfect fit. And when you’re not using them, they come with a carrying case to keep them safe and sound.

Why You Need Custom-Fit Sports Earbuds

  1. If you’re serious about your workouts, you need custom-fit sports earbuds from Bose. With these earbuds, you’ll be able to take your workout to the next level without worrying about them slipping out or getting damaged. Plus, they’re sweat and weather-resistant, so you can take them anywhere. Additionally, they come with a carrying case to keep them secure when not in use.
  2. Custom-fit sports earbuds are also great for people who are always on the go. For example, if you frequently travel for work or pleasure, you know how difficult it can be to find time to work out. But with these earbuds, you can squeeze in a quick workout wherever you are. And because they’re so compact and lightweight, they won’t take up much space in your luggage.
  3. Custom-fit sports earbuds are an investment in your health. They offer superior sound quality to enjoy your music if you suffer hearing loss or damage.

How to Get Custom-Fit Sports Earbuds

If you’re ready to take your workouts to the next level, it’s time to get your own sports earbuds from Bose. No matter what you’re doing, these earphones are made to fit comfortably and securely in your ear. Therefore, these earbuds will stay in position and provide you with the best listening experience, whether you’re exercising, bicycling, or lifting weights.

To get your custom-fit sports earbuds, visit the Bose website and select the “Custom Fit” option. From there, you’ll be able to choose the color, size, and style best suits your needs. And if you have any questions, our team of experts is always here to help.


So, if you’re looking for a way to enhance your workout experience, check out custom-fit sports earbuds from Bose. With these earbuds, you’ll be able to enjoy your music while staying comfortable and protected. So, order them today and see how they can help you take your workouts to the next level! Thanks For Reading!

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How to Find the Perfect Tattoo Shop for You

Are you thinking of getting a tattoo? If so, you need to find the perfect tattoo shop for you. There are many different shops out there, and each one has their own style and atmosphere. It is important that you find a shop that makes you feel comfortable and confident. In this blog post, we will discuss some tips for finding the right tattoo shops Fayetteville NC for you!

Tips for finding the right tattoo shops

  • Know what you want – Before you start your search for a tattoo shop, it is important that you know what kind of tattoo you want. This will help narrow down your options and make it easier to find a shop that specializes in the style of tattoo you are looking for.
  • Do your research – Once you know what kind of tattoo you want, it is time to start doing your research. You can ask friends and family for recommendations, or you can search online for shops in your area. Once you have a list of potential shops, take some time to read reviews and learn more about each one.
  • Visit the shop – After you have done your research and narrowed down your options, it is time to visit the tattoo shops that you are considering. This will give you a chance to see the shop, meet the artist, and get a feel for the overall atmosphere. The shop should be clean and professional, and the artist should be friendly and helpful. You should feel comfortable and confident in your decision to get a tattoo from this shop.
  • Look at the portfolio – Once you have visited the shop and met the artist, it is time to take a look at their portfolio. This will give you a chance to see the artist’s work and decide if they are the right fit for you. The portfolio should be filled with high-quality work that you like.
  • Ask questions – When you visit a tattoo shop, be sure to ask any questions that you may have. This is your chance to learn more about the artist, the process, and anything else you are curious about.  Have a clear idea about what you want before you leave, and be sure that the artist is confident in their ability to create the tattoo you have in mind.
  • Before the tattoo gets inked – Have a look at the final sketch provided by the artist and give your final approval. Make sure that you are happy with the design, size, and placement of the tattoo. The artist should also go over aftercare instructions with you so that you know how to take care of your new tattoo.


Making the decision to get a tattoo is a big one, and it is important that you take the time to find the perfect shop for you. We hope that these tips will help you in your search!

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The Different Types of Search Queries: How to Optimize Your Site for Them All

As a website owner or manager, it’s important to understand the different types of search queries that people use when they’re looking for information online. By understanding the different types of searches, you can optimize your site accordingly and make sure that you’re providing the best possible user experience.

So, what are the different types of search queries? There are four main types of search queries: navigational, informational, transactional, and commercial investigation. Let’s take a closer look at each one:

Navigational searches are used when someone is looking for a specific website or web page. For example, if someone wants to go to the Amazon home page, they would type in “amazon” into their search engine. If someone wants to find a specific article on Wikipedia, they might type in “Wikipedia article on the history of the world.”

Informational searches are used when someone is looking for information on a specific topic. For example, if someone wants to know what the capital of France is, they would type in “capital of France.” If someone wants to learn how to make a cake, they might type in “cake recipe.”

Transactional searches are used when someone is looking to complete a transaction, such as buying a product or booking a hotel room. For example, if someone wants to buy a new pair of shoes, they might type in “shoes” or “buy shoes.” If someone wants to book a hotel room for their vacation, they might type in “hotel rooms” or “book hotel room.”

Commercial investigation searches are used when someone is considering making a purchase, but they want to do more research before committing to anything. For example, if someone is looking for a new car, they might type in “Best cars for 2020” or “cars with good gas mileage.” If someone is looking for a new laptop, they might type in “laptops under $500.”

By understanding the different types of searches that people use, you can optimize your site accordingly and make sure that you’re providing the best possible user experience. So take some time to consider what type of searches your target audience is likely to use, and then make sure that your site is optimized for them.

Some tips on how to optimize your site for different types of searches:

– Use keyword research to identify the most popular search terms that people are using.

– Use these keywords throughout your website, including in the title, meta tags, and body content.

– Create separate pages or sections for each type of search query.

– Use clear and concise titles and descriptions to help people find what they’re looking for.

– Use images, videos, and other visual elements to break up text and make it more visually appealing.

– Make sure your website is mobile-friendly and easy to use on all devices.

By following these tips, you can make sure that your website is optimized for all types of search queries, providing a better user experience for your visitors.

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A Guide to Chinese Halal Food

When it comes to food, there are endless options to choose from. With so many cuisines and dishes available, it can be hard to decide what to eat. However, if you’re looking for a delicious and culturally rich option, you can’t go wrong with halal Chinese food. This blog post will give you a brief overview of halal food and some of the best dishes to try.

What is Halal Food?

Halal food is that which is permissible according to Islamic law. The term “halal” covers not just food and drink, but all aspects of life. In regards to food, it means that the animal has been slaughtered in accordance with Islamic guidelines and that no forbidden ingredients have been used in the dish.

For Muslims, eating halal is a religious obligation. However, halal food is also enjoyed by people of other faiths or no faith at all. That’s because halal food is simply good food! It’s healthy, delicious, and nutritious. Chinese halal cuisine has a long history and has been influenced by both Muslim and non-Muslim cultures over the years. As a result, it is one of the most diverse and interesting types of cuisine available.

Some of the Best Dishes to Try

There are countless fantastic Chinese halal dishes to choose from. However, we’ve compiled a list of some of our favorites for you to try:

  • Mutton Rolls: These delicate little rolls are stuffed with tender shredded mutton that has been cooked in a special sauce. They are then fried until golden brown and served hot with a dipping sauce on the side.
  • Chicken corn soup: This soup is a comforting bowl of chicken broth that is filled with chunks of chicken, sweetcorn, and egg. It’s perfect for a cold winter’s day or anytime you’re feeling under the weather.
  • Sesame prawn toast: This dish consists of deep-fried bread that is topped with shrimp paste and sesame seeds. It can be a starter or served as part of the main course.
  • Beef chow mein: Fresh egg noodles are stir-fried with beef and veggies in a dark soy sauce to make beef chow mein, a traditional Cantonese dish. It is substantial and full but also light enough that you won’t feel sluggish after eating it.
  • Fried aubergine in chili sauce: This dish consists of thin slices of aubergine that are coated in batter and deep-fried until crispy. They are then stir-fried with diced onions, garlic, chilies, and Bok choy in a deliciously spicy sauce.
  • Green tea lava cake: This dessert consists of a soft green tea sponge cake that is filled with molten chocolate lava. It’s rich, indulgent, and absolutely delicious!

Conclusion :

No matter what your tastes may be, there’s sure to be something on this list that will tantalize your taste buds. So next time you’re wondering what to eat, why not give Chinese halal cuisine a try? You won’t be disappointed!

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