The inverse of a symmetric matrix (if it exists) is

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a symmetric matrix

a skew-symmetric matrix

a diagonal matrix

none of these

answer is A.

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Detailed Solution

Let A be an invertible symmetric matrix.We have AA−1=A−1A=In⇒AA−1′=A−1A′=In′⇒A−1′A′=A′A−1′=In⇒A−1′A=AA−1′=InA−1′=A−1 [inverse of a matrix is unique]

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