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October 25th, 2014, 01:45 PM  #1 
Newbie Joined: Oct 2014 From: Edinburgh, Scotland Posts: 3 Thanks: 0  Proof with symmetric and invertible matrix
Qu. Prove that if a symmetric matrix is invertible, then its inverse is symmetric also. So far I have this.. is it correct? $\displaystyle A=A^T \\ A^{1}A=A^{1}A^T\\ \mathbb{I}=A^{1}A^T\\ \mathbb{I}{(A^T)}^{1}=A^{1}A^T{(A^T)}^{1}\\ {(A^T)}^{1}=A^{1}\mathbb{I}\\ {(A^T)}^{1}=A^{1}\\ $ Last edited by iluvmafs; October 25th, 2014 at 01:50 PM. 
October 25th, 2014, 02:01 PM  #2  
Senior Member Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116  Quote:
 
October 25th, 2014, 02:38 PM  #3 
Newbie Joined: Oct 2014 From: Edinburgh, Scotland Posts: 3 Thanks: 0  
October 25th, 2014, 02:51 PM  #4 
Newbie Joined: Oct 2014 From: Edinburgh, Scotland Posts: 3 Thanks: 0 
So to prove this, do I have to show that $\displaystyle A^{1}={(A^{1})}^T $? Last edited by iluvmafs; October 25th, 2014 at 02:57 PM. 

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invertible, matrix, proof, symmetric 
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