IPMAT Indore 2024 (SA) PYQs

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 $A = \begin{bmatrix} 1 & 2 \newline 3 & a \end{bmatrix}$ 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 _________