# Operations On Matrix | Transpose of a Matrix and Inverse of Matrix

There are 3 main operations on the matrix

- Addition
- Subtraction
- Multiplication

**Addition of matrices:**

Two matrices A and B can be added if they have the same orders and their corresponding entries are added.

**Example:**

**Subtraction of Matrices:**

Two matrices A and B can be subtracted if they have the same orders and their corresponding entries are subtracted.

**Multiplication of Matrices:**

Matrix multiplication or multiplication of matrices is one of the operations that can be performed on matrices in linear algebra.

If A and B are two given matrices then the multiplication of these matrices is possible, if A and B are compatible.

Matrix multiplication is a binary operation, that gives a matrix from two given matrices.

A and B matrices are said to be compatible if the number of columns of the A matrix is equal to the number of rows of matrix B.

**Example**:

**Transpose of the matrix:**

The transpose of a matrix is obtained by changing the rows into columns and columns into rows. Transpose of a matrix is denoted by A^{t}.

For example, if we have a matrix A

In this matrix, there are 3 rows and 3 columns. The rows will convert into columns and columns into rows.

**Negative of a matrix:**

If we have a matrix A,

Negative of A is obtained by changing the sign of each entry of A. The negative of A is denoted by –A.

**Inverse of Matrix:**

If we have a matrix A, the inverse of the matrix will be,

The inverse of the matrix is denoted by A^{-1.}

## Frequently Asked Question-FAQs

### What are the basic operations in matrices?

The three most common matrix operations are addition, subtraction, and multiplication of matrices.

### what is Transpose of Matrix?

The transpose of a matrix is a new matrix that is formed by exchanging the rows and columns of the original matrix.

### Is matrix addition commutative?

Yes. Matrix addition is commutative

### Is matrix multiplication commutative?

No. Matrix multiplication is not commutative.

### Is matrix addition associative?

Yes. Matrix addition is associative.

### What is the product of a matrix with a null matrix?

A matrix that has been multiplied by a null matrix will always result in a null matrix.

## Leave a Reply