Dr. Giarusso's Problem:

Suppose * is an associative operation on a set S, and A, B, and C are three elements of S such that

A*B=B*A
A*C=C*A
A*B*A=A, and
B*A*B=B

Prove that B*C=C*B.

Recall that * is associative means that X*(Y*Z)=(X*Y)*Z

Due Friday, April 6^th at Noon.