(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Determine which of the formulas hold for all invertible nxn matrices A and B

A. AB=BA

B. (A+A^–1)^8=A^8+A^–8

C. A^5 is invertible

D. A+A^–1 is invertible

E. (In+A)(In+A^–1)=2In+A+A^–1 (where In is the identity matrix)

F. (A+B)^2=A^2+B^2+2AB

2. Relevant equations

Certain properties of inverse matrices can be used. For example, if A is invertible, then A^k is invertible for all k greater or equal to 1 (this proves C to be correct).

3. The attempt at a solution

I was able to find counterexamples to prove A and B and F incorrect. However, the webwork program (designed for practicing basic Linear Algebra) I am using states that C, D, and E are not all correct ... what am I missing?

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# Homework Help: Properties of Inverse Matrices

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