Statistics and Probability: JEE Main 2025 Mathematics question

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