Prove that A is idempotent if and only if AT is idempotent. Getting Started: The phrase "if and only if" means that you have to
prove two statements. 1. If A is idempotent, then AT is idempotent. 2. If AT is idempotent, then A is idempotent. STEP 1: Begin your proof of the first statement by assuming that A is idempotent.