The problem is:
"The $2\times 2$ matrix A satisfies $A^2-4A-7I=0,$ where I is the $2\times 2$ identity matrix. Prove that A is invertible."
The hint given is:
"We are trying to a matrix that is the inverse of A."
I completed the square and was proceeding to take the square root of both sides when I realized the identity matrix has multiple square roots.