Matrix Similarity Proof - need someone to check if it's correct

[jumbogala]

Homework Statement

My textbook has no answers so I was wondering if someone could let me know if I'm right.

The question: A and B are m x n matrices.
Let A = I. Find when B = A.

Homework Equations

The Attempt at a Solution

What I did seems too easy:

If B ~ A, then A ~ B (this is just a property of similarity)

Since A = I, we can sub in for A

So B = A

Did I just argue myself in circles?

 

[Dick]

That's fine. You can take the 'I' out because IP=P. 'I' is the identity matrix.

 

[jumbogala]

Great, thank you! Do you think it's necessary to show that if A ~ B, B ~ A?

 

[Dick]

Great, thank you! Do you think it's necessary to show that if A ~ B, B ~ A?

If you're not clear on why it's true, you should probably show it. It's easy enough.