The inverse of symmetric matrix is??

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Answer 1 · 2018-07-30T11:32:44

Please see the explanation below.

Let the square matrix $A$ be invertible

Then,

$AxxA^-1=I$

where $I$ is the identity matrix.

If $A$ is a symmetric matrix, then

$A=A^T$

$A^-1=(A^T)^-1$

since for all square matrices

$(M^-1)^T=(M^T)^-1$

Therefore

$A^-1=(A^-1)^T$