IPMAT Indore (MCQ) PYQs

Suppose $a, b$ and $c$ are integers such that $a>b>c>0$, and $A=\left[\begin{array}{lll}a & b & c \\ b & c & a \\ c & a & b\end{array}\right]$. Then the value of the determinant of $A$ is

A $2 \times 2$ matrix is filled with four distinct integers randomly chosen from the set $\{1,2,3,4,5,6\}$. Then the probability that the matrix generated in such a way is singular is

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