# Matrices Inverse properties

thepassenger48

## Homework Statement

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

1. (A+A^-1)^7 = A^7+A^-7
2. 2A is invertible
3. (A+B)² = A² + B² + 2AB
4. (ABA^-1)^6 = AB^6A^-1
5. A + B is invertible
6. ABA^-1 = B

I know 2A should be invertible, and number 3 wrong, but what else?
Thanks

Homework Helper
Try to think of examples if a fact bothers you or if you can't proove it.

Homework Helper
For 1) and 3, write out the computation- for 1 you might want to look at (A+ A-1)2 first.

For 5, if A is invertible, then so is B= -A.

Staff Emeritus