IPMAT Indore 2019 (SA) PYQs

If $A = \begin{bmatrix} 1 & 2 \newline 3 & a \end{bmatrix}$ where $a$ is a real number and det $(A ^ 3 - 3A ^ 2 - 5A) = 0$ then one of the values of $a$ can be

If $A = \begin{bmatrix} 2 & n \\ 4 & 1 \end{bmatrix}$ such that $A^3 = 27 \begin{bmatrix} 4 & q \\ p & r \end{bmatrix}$, then $p + q + r$ equals _________

If $A=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0\end{array}\right]$, then the absolute value of the determinant of $\left(A^{9}+A^{6}+A^{3}+A\right)$ is __________.