I'm not too good with matrix equations and how to go about solving or even just simplifying them. An example from my text book is:
"Suppose that A is a square matrix of size n x n that satisfies the the matrix equation
A15ATA14 + 72A6(AT)2A5 + 16AATA3 - 7I = 0
Show that the matrix A is invertible and find an expression for A-1 in terms of A"
How can I go about solving this? I don't even know where to start :S
Therefore, any help would be greatly appreciated.