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Suppose A and B are invertible matrices, with A being m x m and B being...

Suppose A and B are invertible matrices, with A being m x m and B being n x n. For any m x n matrix C and any n x m matrix D, show that :

a) (A + CBD)-1 = A-1- A-1C(B-1 + DA-1C)-1DA-1

b) If A, B and A + B are all m x m invertible matrices, then deduce from (a) above that (A + B)-1 = A-1 - A-1(B-1 + A-1)-1A-1

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