(adsbygoogle = window.adsbygoogle || []).push({}); Proof involving nonsingular matrices.

1. The problem statement, all variables and given/known data

If (I + A) is nonsingular, prove that (I - A)(I + A)^{-1}= (I + A)^{-1}(I - A), and hence (I - A)/(I + A) is defined for the matrix.

I've proved it like this:

Let (I - A)(I + A)^{-1}= A, and (I + A)^{-1}(I - A) = B.

B^{-1}= (I - A)^{-1}(I + A)

B^{-1}A = I

Premultiplying by B, we get A = B.

Is this proof correct?

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# Homework Help: Eigenvalue of a matrix.

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