A(a^{14}a^{t}a^{14} + 72a^{5}(a^{t})^{2}a^{5} + 16a^{t}a^{3}) = 7I
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
A^{15}A^{T}A^{14} + 72A^{6}(A^{T})^{2}A^{5} + 16AA^{T}A^{3} - 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.
Thanks,
Mark