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# What are the matrix operations?

## Overview– matrix operations

A matrix is the rectangular arrangement of arrays, that we arrange in rows and columns. the term “Matrix” was coined by James Joseph Sylvester in 1850.

In this blog, We are going to discuss about the matrix operations

## Definition of matrix

It is a rectangular arrangement of numbers that we form by keeping them in m numbers of rows and n numbers of columns.

## Algebra of Matrices– matrix operations

let’s discuss about the matrix operations-

1.     Addition and subtraction of matrices:

Addition and subtraction of matrices is possible if and only if they are of same order.

We add or subtract the corresponding elements of the matrices.

1.     Scalar multiplication of matrices:

In this, we multiply the scalar or constant with each element of the matrix.

For example,

2.     Multiplication of matrices: We can multiply two matrices only if they are conformal i.e. the number of columns of the first matrix is equal to the number rows of the second matrix.

For example:

1.     Power of Matrices: If A is A square matrix then

and so on.

If where A is square matrix then it is said to be idempotent.

5.Transpose of  a  matrix: The  matrix that we obtain from any given  matrix A ,  by interchanging rows  and   columns is  called  the  transpose of  A and is  denoted  by

here, the transpose of matrix

## Types of matrices

Row matrix:

A matrix with only one single row and many columns is possible.

Column matrix

A matrix with only one single column and many rows can be possible.

Square matrix

Square matrix- A matrix in which the number of rows is equal to the number of columns.

Thus an m by n matrix is a square matrix then m = n and is said to be of order n.

The determinant having the same elements as the square matrix A is called the determinant  of  the matrix A. denoted by |A|.

The diagonal elements of matrix A are 2, 2 and 1 is the leading and the principal diagonal.

The sum of the diagonal elements of square matrix A is called the trace of A.

A square matrix is a singular if its determinant is zero otherwise non-singular

For example:

Hence the square matrix A is   non-singular.

Diagonal matrix

A square matrix is a diagonal matrix if all its non diagonal elements are zero.

Scalar matrix:

A  diagonal  matrix is a scalar matrix if  its diagonal  elements  are equal.

Identity matrix:

A square matrix in  which elements in  the diagonal  are all 1  and the rest are all zero  is  called  an  identity matrix  or Unit matrix.

Null Matrix:

If all the elements of a matrix are zero, then it is a null or zero matrix.

Ex:    etc.

Symmetric matrix:

A square matrix is a symmetric matrix if its transpose is equal to the matrix itself.

For example:

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