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 $A$. Then (1) $(P)$ is false and $(Q)$ is true (2) Both $(P)$ and $(Q)$ are false (3) $(P)$ is true and $(Q)$ is false (4) Both $(P)$ and $(Q)$ are true
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 $A$. Then\\
(1) $(P)$ is false and $(Q)$ is true\\
(2) Both $(P)$ and $(Q)$ are false\\
(3) $(P)$ is true and $(Q)$ is false\\
(4) Both $(P)$ and $(Q)$ are true