If AB is idempotent with A an m×n matrix and B an n×m matrix, is BA idempotent?

[tghg]

A difficult problem about linear algebra.Help!

Suppose that A is a m*n matrix，B is a n*m matrix,and AB is a idempotent matrix.
Please verify that BA is also a idempotent matrix.

 

[StatusX]

Do you know what an idempotent matrix is? Where are you getting stuck?