When I try to solve the equation $A^2-5A-4I=o$ for any square matrix A and its compatible identity matrix, I factored the euqation's left into $(A-\frac{5}{2}I)^2=\frac{41}{4}I^2$ so that the answer should be $A = \frac{5\pm\sqrt{41}}{2}I$.
What have I done above is right?