Let A be a 2 × 2 real matrix with entries from {0,1} and | A | ≠ 0. Consider the following two statements: (P) If A ≠ I_2, then | A |=-1 (Q) If | A…

Let $\displaystyle A$ be a $\displaystyle 2 \times 2$ real matrix with entries from $\displaystyle \{0,1\}$ and $\displaystyle |\mathrm{A}| \neq 0$. Consider the following two statements : (P) If $\displaystyle \mathrm{A} \neq \mathrm{I}_2$, then $\displaystyle |\mathrm{A}|=-1$ (Q) If $\displaystyle |\mathrm{A}|=1$, then $\displaystyle \operatorname{tr}(\mathrm{A})=2$, where $\displaystyle \mathrm{I}_2$ denotes $\displaystyle 2 \times 2$ identity matrix and $\displaystyle \operatorname{tr}(\mathrm{A})$ denotes the sum of the diagonal entries of A. Then :