IPMAT Indore 2019 (SA) PYQs

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 $A$ 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 $A=\left[\begin{array}{ll}1 & 0 \\ \frac{1}{2} & 0\end{array}\right]$ then $A^{2022}$ is