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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 \( \mathrm{A} \neq \mathrm{I}_{2} \), then \( |\mathrm{A}|=-1 \)
(Q) If \( |A|=1 \), then \( \operatorname{tr}(\mathrm{A})=2 \),
where \( \mathrm{I}_{2} \) denotes \( 2 \times 2 \) identity matrix and \( \operatorname{tr}(\mathrm{A}) \) denotes the sum of the diagonal entries of \( A \).
Then:
(a) \( (\mathrm{P}) \) is true and \( (\mathrm{Q}) \) is false
(b) Both \( (\mathrm{P}) \) and \( (\mathrm{Q}) \) are false
(c) Both \( (\mathrm{P}) \) and \( (\mathrm{Q}) \) are true
(d) \( (\mathrm{P}) \) is false and \( (\mathrm{Q}) \) is true
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