Matrix Inverse Identity Proof help

buddy549

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Oct 6, 2016
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I do not know how to go about this problem.

Let A, B and A+B be non-singular matrices. Prove that A-1+B-1 is non singular by showing that:

(A-1+B-1) -1= A(A+B)-1​B
 
I do not know how to go about this problem.

Let A, B and A+B be non-singular matrices. Prove that A-1+B-1 is non singular by showing that:

(A-1+B-1) -1= A(A+B)-1​B
Do you know how to take inverses of products? That is
(AB)-1 = B-1 A-1
If not, proving that may help.
 
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