If $A=\left[\begin{array}{cc}2 & -3 \\ 3 & 4\end{array}\right]$ then, the value of $A^2-6 A$.

$-17 I$, where I is an identity matrix of order 2

The correct answer is Option (4) → $-17 I$, where I is an identity matrix of order 2

$A^2=\left[\begin{array}{cc}2 & -3 \\ 3 & 4\end{array}\right]\left[\begin{array}{cc}2 & -3 \\ 3 & 4\end{array}\right]=\left[\begin{array}{cc}-5 & -18 \\ 18 & 7\end{array}\right]$

$A^2-6A=\left[\begin{array}{cc}-5 & -18 \\ 18 & 7\end{array}\right]-\left[\begin{array}{cc}12 & -18 \\ 18 & 24\end{array}\right]=-17I_2$