Okay so I was practicing proofs and the following appeared in my book. i'm confused as to how do it so i would be thankful for any help: Let A be a symmetric nonsingular matrix. Prove that its inverse (A^-1) is symmetric.
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Originally Posted by buckaroobill Okay so I was practicing proofs and the following appeared in my book. i'm confused as to how do it so i would be thankful for any help: Let A be a symmetric nonsingular matrix. Prove that its inverse (A^-1) is symmetric. Let * mean transpose. We know that, A*=A Because it is symettric. We need to show, (A^-1)*=A^-1 (1) You can use the fact that, (M^-1)*=(M*)^-1 For non-singular matrices. But that means in (1) we have, (A^-1)*=(A*)^-1=A^-1 Thus, it is symmettric.
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