The following is an old exam question I'm trying solve but I just can't. Any help would be much appreciated. The teachers has provided answers to all questions on the exam besides this one..
A quadratic matrix $B$ satisfies the equation $B^2 + B - I = 0$ where $I$ is an identity matrix with dimensions $N\times N$ and where $0$ is the null matrix with the dimensions $N\times N$.
a) What size is the matrix $B$?
b) Show that $I + B$ is the inverse matrix of $B$.
c) Show that $B^3 = -I + 2B$.