- #1
CuppoJava
- 24
- 0
Homework Statement
Prove that given a matrix A, and A^2 = A, then A must be either the zero matrix or the identity matrix.
The Attempt at a Solution
By multiplying both sides by A, you can deduce that A = A^2 = A^3 = A^4 ...
From there I think it's obvious that A must be either 0 or I, but I don't know how to start proving it formally.
Thanks very much for your help
-Patrick