#### Provide solution for RD Sharma maths class12 Chapter Algebra of Matrices exercise 4.3 question 3 sub question (iii)

AB=11 and $BA =\begin{bmatrix} 0 &0 &0 &0 \\ 1& -1 & 2 &3 \\ 3 &-3 &6 &9 \\ 2 &-2 &4 &6 \end{bmatrix}$

Hint: matrix multiplication is only possible, when number of columns of first matrix is equal to the number of rows of second matrix.

Given: $A=\begin{bmatrix} 1 &-1 &2 & 3 \end{bmatrix}$  and$B=\begin{bmatrix} 0\\ 1\\ 3\\ 2 \end{bmatrix}$

Consider,

$AB=\begin{bmatrix} 1 &-1 &2 & 3 \end{bmatrix}\begin{bmatrix} 0\\ 1\\ 3\\ 2 \end{bmatrix}$

$AB=[ 1 \times 0 +(-1)\times 1 +2\times 3+3\times 2]$

$AB=[ 0-1+6+6]$

$AB=11$

Again consider,

$BA=\begin{bmatrix} 0\\ 1\\ 3\\ 2 \end{bmatrix}\begin{bmatrix} 1 &-1 &2 & 3 \end{bmatrix}$

$B A=\left[\begin{array}{cccc} 0 \times 1 & 0 \times-1 & 0 \times 2 & 0 \times 3 \\ 1 \times 1 & 1 \times(-1) & 1 \times 2 & 1 \times 3 \\ 3 \times 1 & 3 \times(-1) & 3 \times 2 & 3 \times 3 \\ 2 \times 1 & 2 \times(-1) & 2 \times 2 & 2 \times 3 \end{array}\right]$

$BA =\begin{bmatrix} 0 &0 &0 &0 \\ 1& -1 & 2 &3 \\ 3 &-3 &6 &9 \\ 2 &-2 &4 &6 \end{bmatrix}$