If $A=\left[\begin{array}{ll}3 & -5 \\ 4 & -7\end{array}\right]$, then $A^{-1}$ is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $\left[\begin{array}{ll}7 & -5 \\ 4 & -3\end{array}\right]$
$A=\left[\begin{array}{ll}3 & -5 \\ 4 & -7\end{array}\right]$
$|A|=3(-7)-(-5)(4)=-1$
$adj\,A=\left[\begin{array}{ll}-7 & 5 \\ -4 & 3\end{array}\right]$
So $A^{-1} = \frac{1}{-1} \begin{bmatrix} -7 & 5 \\ -4 & 3 \end{bmatrix} = \begin{bmatrix} 7 & -5 \\ 4 & -3 \end{bmatrix}$