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Linear Algebra question:Suppose A and B are invertible matrices,with A being m*m and B n*n.For any...

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

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

b) If A,B and A+B are all m*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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