If \( A \) is a matrix such that \( A^{2}+A+2 I=O \), then which of the following is/are true?....

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If \( A \) is a matrix such that \( A^{2}+A+2 I=O \), then
P
which of the following is/are true?
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(1) \( A \) is nonsingular
(2) \( A \) is symmetric
(3) A cannot be skew-symmetric
(4) \( A^{-1}=-\frac{1}{2}(A+I) \)


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