Orthogonal matrix whose submatrix has special properties

[julie94]

Dear Forumers.

I am working on the following problem.

Let matrix P=( A B ) where A and B are matrices. Let P be an n*n orthogonal matrix.

Show that A'A is an idempotent matrix.

I do not know where to start. Thanks in advance for the help.

 

[julie94]

I can write
PP'=(A B)(A B)'
=(AB'+AA' BB' +BA')

and I can write
PP'=In