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## Homework Statement

Prove that if matrices A and b are similar and A is diagonalizable, then B is diagonalizable.

## Homework Equations

this shows that A and B are similar i believe

A = [P]

**[P]^-1**

and

D = [P]^-1 [A] [P]

means A is diagonalizable

I believe this is a simple proof but i want to know the reason behind each step of the proof.

this is what i've tried D =[p]^-1 ([P]

and

D = [P]^-1 [A] [P]

means A is diagonalizable

## The Attempt at a Solution

I believe this is a simple proof but i want to know the reason behind each step of the proof.

this is what i've tried D =[p]^-1 ([P]

**[P]^1)[P]**

what i did was plug in A from the first equation into the second so i would get

[D]=what i did was plug in A from the first equation into the second so i would get

[D]=

**? this this right?**