Recent content by tigger1989

Homework Statement 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 Homework Equations...

Hi, I'm a little rusty on Linear Algebra, so forgive my ignorance on some of the approaches. Can you elaborate by what you mean by "trivial"? I tried random matrices (often with easy numbers, such as the identity matrix) for A, B, C, D, E, and F, but only found counterexamples for A, B, and F...

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 I was able to find counterexamples to prove A and B...