Show that if a square matrix A satisﬁes the equation ....then A must be invertible. 
(a) Show that if a square matrix $A$ satisfies the equation $A^2 + 2A + I = 0$, then $A$ must be invertible. What is the inverse?
(b) Show that if $p(x)$ is a polynomial with a nonzero constant term, and if $A$ is a square matrix for which $p(A) = 0$, then $A$ is invertible.

What am i supposed to do here? plug a square matrix with a b c d in the problem?.. but then what? and i dont have a clue how to do the second one either...

If $A$ is not invertible, then $0$ is an eigenvalue of $A$. Thus, $p(0)$ must be an eigenvalue of $p(A) = 0_{n\times n}$. But all of the eigenvalues of $p(A) = 0_{n\times n}$ are $0$. So, we must have $p(0) = 0$. This is a contradiction since $p$ has a non-zero constant term, and so, $p(0) \neq 0$. Therefore, $A$ is invertible, as desired. 
