IPMAT Indore 2019 (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 $3 \times 3$ matrix is filled with +1's and -1's such that the sum of each row and column of the matrix is 1, then the absolute value of its determinant is

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