Let $A$ be a $2 \times 2$ real matrix with entries from $\{0,1\}$ and $|A|\neq 0$. Consider the following two statements: (P) If $A \neq I_2$, then $|A| = -1$ (Q) If $|A| = 1$, then $\operatorname{tr}(A) = 2$ where $I_2$ denotes $2 \times 2$ identity matrix and $\operatorname{tr}(A)$ denotes the sum of the diagonal entries of $A$.