Permutation Matrices: Proving P Inverse = P Transpose

[EvLer]

I can't proove why P inverse = P transpose always!
P is the permuation matrix, i.e. a matrix is identity but the rows can be interchanged.
Thanks in advance.

 

[matt grime]

I can offer no other advice than that you should just write down PP^t (the rows of P are an ******* basis of R^n - fill in the *******).