1. ## [SOLVED] Eigenvalues

Let A be a real 2x2 matrix.
If A has two distinct eigenvalues, then ${A^2 }$ has two distinct eigenvalues.

False, does anyone know a counterexample or relevant theorem of definition?

2. Originally Posted by dwsmith
Let A be a real 2x2 matrix.
If A has two distinct eigenvalues, then ${A^2 }$ has two distinct eigenvalues.

False, does anyone know a counterexample or relevant theorem of definition?
If $\lambda$ is an eigenvalue of $A$ then $\lambda^2$ is an eigenvalue of $A^2$

Now you just need a 2 by 2 matrix eigenvalue $\pm 1$.