If $A=\left[\begin{array}{ll}3 & -5 \\ 4 & -7\end{array}\right]$, then $A^{-1}$ is:

$\left[\begin{array}{ll}7 & -5 \\ 4 & -3\end{array}\right]$

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 $A^{-1}=\frac{adj\,A}{|A|}=\left[\begin{array}{ll}-7 & 5 \\ -4 & 3\end{array}\right]$