Matrix Inverse Identity Proof help

[buddy549]

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

 

[Ishuda]

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.

 

[Ishuda]

plz explain...

Just to be a little bit more helpful, take inverses of both sides.