1. The problem statement, all variables and given/known data Show that if a square matrix A satisfies A3 + 4A2 -2A + 7I = 0 Mod note: It took me a little while to realize that the last term on the left is 7I, seven times the identity matrix. The italicized I character without serifs appeared to me to be the slash character /. then so does AT 2. Relevant equations 3. The attempt at a solution What I notice is that for any n x n matrix A and powers thereof, the diagonals of A and the transpose are the same. I experimented with a 2 x 2 matrix (with entries a, b, c, d), squared and cubed to see what happens and the result, aside from being somewhat messy, ends with each matrix reducing to I when appropriate row operations are applied. I'm not sure how to proceed from here or if I'm even on the right track with this thinking. Please assist.