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 |

### Determinant

Let A be a square matrix of order two having elements a_{11}, a_{12}, a_{21}, a_{22}. To calculate the determinant, we multiply a_{11} and a_{22}. Then, multiply a_{21} and a_{12}. Then, find the difference (a_{11}a_{22} – a_{21}a_{12}). 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.