# Matrices: Types of Matrices

## What is Matrices?

A matrix is the arrangement of some elements or numbers in rows and columns.

Horizontal lines of elements are called rows of the matrix while the vertical lines of elements are called columns of the matrix.

The elements of a matrix are enclosed by bracket() or [].

Matrix having m rows and n columns is called an m x n containing mn elements in it.

The order of this matrix is m x n.

It is denoted by A=[a _{ij}]

## Addition & subtraction of Matrices

Addition & subtraction of Matrices two matrices is possible when the order of two matrices are same and their solution is also a matrix of same order.

## Multiplication of Matrices

Multiplication of two matrices A and B is defined only when the number of column of A is equal to the numbers of rows of B.

If the number of columns of A is different from number of rows of B, then the product AB is not define.

**(2, 1, 4) • (4, 2, 3) = 2×4 + 1×2 + 4×3**

**= 22**

## Transpose Matrix

A matrix obtained by interchanging the rows and columns is called Transpose of a Matrix. If A is any matrix of order m x n, then its transpose denoted by A’ OR A^{T }is of order n x m.

**Also (i,j)th element of A = (j,i)th element of A’ OR A ^{T}**