Please see the attached document for homework specifics. Thank-you.
Suppose that A and B are invertible n x n matrices
A. Show that if c ≠ 0, then cA is invertible. Justify your answer, using the definition of an invertible matrix.
What is (cA)-1 ?
B. Must A + B be invertible? If so, show that is it; if not give an example where it fails (and A and B are 2 x 2 or larger).
This is a matrix theory problem that proves whether or not given matrices are invertible.