Ok so I have this question I have had some problem solving (I've done part 1.):
We have two $n \times n$ matrices $A$ and $B$ and it says that $A=I-AB$.
Prove that $A$ is regular and $AB=BA$. (done this one is pretty easy)
Prove that if $B$ is symmetrical, so is $A$.
Prove that $B^3=0$ if and only if $A=I-B+B^2$.
Thanks in advance...