This is one problem I've been tackling for a while:
If A, B, and A+B are all invertible matrices of order "n", prove that is invertible and that:
First, is there a generic formula for ? (If so, our instructor never taught us one). I'm also assuming that we can't assume AB is commutable, because that could make everything so much easier. ^_^;
Anyway. Any helpful hints might help. Basically what I've tried to do so far is equate the "middle" and RHS statements by multiplying both sides by inverses to isolate , but I don't really see how that 'proves' anything ...