
Linear Algebra Linear Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
October 25th, 2014, 02:45 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 02:50 PM. 
October 25th, 2014, 03:01 PM  #2  
Senior Member Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116  Quote:
 
October 25th, 2014, 03:38 PM  #3 
Newbie Joined: Oct 2014 From: Edinburgh, Scotland Posts: 3 Thanks: 0  
October 25th, 2014, 03:51 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 03:57 PM. 

Tags 
invertible, matrix, proof, symmetric 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Why Isn't This Matrix Invertible?  Magnesium  Linear Algebra  2  December 11th, 2013 03:09 AM 
invertible matrix  shine123  Linear Algebra  1  September 21st, 2012 09:47 AM 
matrix invertible problem  frankpupu  Linear Algebra  3  March 6th, 2012 12:45 PM 
Invertible matrix  problem  Linear Algebra  3  August 31st, 2011 06:30 AM 
Find an invertible matrix P  450081592  Linear Algebra  1  June 24th, 2010 08:13 AM 