# Similar matrices

1. Nov 19, 2007

### eyehategod

can anyone guide me through this proof?

prove that if A is idempotent and B is similar to A, then B is idempotent.(Idempotent A=A^2)

2. Nov 19, 2007

### varygoode

So, let's think about this. If B is similar to A, then what? For some invertible matrix (of appropriate dimensions) we have:

$$A$$ = $$P^{-1}$$ $$*B*P$$.

Consider what $$A^2$$ is and remember $$A$$ = $$A^2$$.

Last edited: Nov 19, 2007
3. Nov 20, 2007

### ritzy

Hi everyone,

-Show that if the square matrix B is similar to the square matrix A...

-then B^k is similar to A^k for any positive integer k
-if A is invertible, then B is invretible and B^-1 is similar to A^-1

Thank you so much!!

4. Nov 20, 2007

### matt grime

What are the definitions (read post 2). It all follows from them directly.