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If \( A \) is a \( 2 \times 2 \) matrix and \( A^{2}=I \) where \( A \neq I \),
\( \mathrm{P} \) \( A \neq-I \) then which of the following is necessarily

W true?
(A) \( \operatorname{Tr}(\mathrm{A})=0 \) and \( |\mathrm{A}|=1 \) or -1
(B) \( \operatorname{Tr}(\mathrm{A})=0 \) and \( |\mathrm{A}|=1 \)
(C) \( \operatorname{Tr}(\mathrm{A}) \neq 0 \) and \( |\mathrm{A}|=-1 \)
(D) \( \operatorname{Tr}(\mathrm{A})=0 \) and \( |\mathrm{A}|=-1 \)
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