IPMAT Indore (SA) PYQs

Let $A, B, C$ be three $4 \times 4$ matrices such that $det \ A = 5, det \ B = -3$, and $det \ C = \frac{1}{2}$. Then the $det$ $2AB^{-1}C^3B^T$ 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 $3 \times 3$ 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