IPMAT Indore 2022 (MCQ) PYQs

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 $A, B$ and $A + B$ are non singular matrices and $AB = BA$ then $2A - B - A(A + B)^{-1}A + B(A + B)^{-1} B$ 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 __________.