Question

If $A$ is a matrix of order $3\times 4$ and $B$ is a matrix of order $4\times 3,$ find the order of the matrix of $AB.$

Answer 1

$\left[\begin{array}{c}\text{If}X=[x_{ij}{]}_{m\times n}\text{and}Y=[y_{ij}{]}_{p\times q}\text{be two}\\ \text{matrices of order}m\times n\text{and}p\times q.\text{Then}\\ \text{multiplication of matrices}X\text{and}Y\text{is defined}\\ \text{if number of columns of}X\text{is same as the}\\ \text{number of rows of}Y\text{i.e.,}n=p.\text{Also},\\ XY\text{is a matrix of order}m\times q.\end{array}\right]$

Given: $A$ is a matrix of oredr $3\times 4$ and $B$ is a

matrix of order $4\times 3$

Here, no . of columns in $A=$ no . of rows in $B$

So, product $AB$ is defined.

And order of $AB$ is $3\times 3.$