Let A =[ a_i j] be a 2 × 2 matrix such that a_i j ∈{0,1} for all i and j. Let the random variable X denote the possible values of the determinant of…

Let $\displaystyle \mathrm{A}=\left[\mathrm{a}_{i j}\right]$ be a $\displaystyle 2 \times 2$ matrix such that $\displaystyle \mathrm{a}_{i j} \in\{0,1\}$ for all $\displaystyle i$ and $\displaystyle j$. Let the random variable X denote the possible values of the determinant of the matrix A. Then, the variance of X is :