Question: Suppose that A, B, A+B are all nonsingular pxp matrices. Show that A -1 + B -1 is also nonsingular, and that (A -1 +B

Suppose that A, B, A+B are all nonsingular pxp matrices. Show that A^-1+ B^-1is also nonsingular, and that (A^-1+B^-1)^-1= A(A+B)^-1B and that this in turn equals B(A+B)^-1A.

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