Question

The inverse of symmetric matrix is??

Answer 1

Please see the explanation below.

Explanation:

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`