If $A = \begin{bmatrix} 2 & 1 \\ 5 & 3 \end{bmatrix}$ and $B^{-1} = \begin{bmatrix} 4 & -5 \\ -3 & 4 \end{bmatrix}$ then $(AB)^{-1}$ is equal to
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $\begin{bmatrix} 37 & -14 \\ -29 & 11 \end{bmatrix}$ ##
$(AB)^{-1} = B^{-1} A^{-1}$
$= \begin{bmatrix} 4 & -5 \\ -3 & 4 \end{bmatrix} \begin{bmatrix} 3 & -1 \\ -5 & 2 \end{bmatrix}$
$= \begin{bmatrix} 37 & -14 \\ -29 & 11 \end{bmatrix}$