Lie theory question

From: Chen Wei (alcatraz_at_gmail.com)
Date: 01/26/05 

Date: Tue, 25 Jan 2005 23:04:30 -0700

 Let $G$ be a complex simple Lie group, $G=KP$ a Cartan decomposition,
 $A\subset P$ maximal abelian, $a\in A$, $p\in P$ such that $pap\in A$.
 Prove that $p\in A$.
 (And there I do mean $pap$, not $pap^{-1}$.) Many thanks in advance.