If $A =\begin{bmatrix}1&2&3\\-4&-5&-2\end{bmatrix}, B=\begin{bmatrix}2&-3\\4&-5\\2&-1\end{bmatrix}$ and $BA = [b_{ij}]$, then $(b_{23}-b_{31})$ is equal to

16

The correct answer is Option (3) → 16

Given matrices:

$A = \begin{bmatrix} 1 & 2 & 3 \\ -4 & -5 & -2 \end{bmatrix}$, $B = \begin{bmatrix} 2 & -3 \\ 4 & -5 \\ 2 & -1 \end{bmatrix}$

Compute $BA$:

$BA = \begin{bmatrix} 2 & -3 \\ 4 & -5 \\ 2 & -1 \end{bmatrix} \begin{bmatrix} 1 & 2 & 3 \\ -4 & -5 & -2 \end{bmatrix}$

$BA = \begin{bmatrix} 14 & 19 & 12 \\ 24 & 30 & 22 \\ 6 & 9 & 4 \end{bmatrix}$

Then, $(b_{23} - b_{31}) = 22 - 6 = 16$

Therefore, $(b_{23} - b_{31}) = 16$.