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If $\mathrm{A}$ is a symmetric matrix with real entries, then
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Verified Answer
The correct answer is:
$\mathrm{A}^{-1}$ is symmetric, if it exists
If $A$ is symmetric then $A^T=A$
$$
\left(A^{-1}\right)^T=\left(A^T\right)^{-1}=A^{-1}
$$
$\therefore \quad A^{-1}$ is also symmetric.
$$
\left(A^{-1}\right)^T=\left(A^T\right)^{-1}=A^{-1}
$$
$\therefore \quad A^{-1}$ is also symmetric.
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