IPMAT Indore (SA) PYQs

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 __________.

If $A$ is a $3 \times 3$ non-zero matrix such that $A^2 = 0$ then the determinant of $(I + A)^{50} - 50A$ is equal to

If inverse of the matrix $\left[\begin{array}{cc}2 & -0.5 \\ -1 & x\end{array}\right]$ is $\left[\begin{array}{ll}1 & 1 \\ 2 & 4 \end{array}\right]$, then the value of $x$ is