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