Question
Wed March 14, 2012 By:

PROVE

Expert Reply
Thu March 15, 2012

It is given that:

AB = A, BA = B

BTAT = AT, ATBT = BT        … (1)

Now, (AT)2 = AT. AT

                 = BTAT. BTAT    [From (1), AT = BT AT]

                 = BT BT AT         [From (1), AT BT = BT]

                 = BT AT              [From (1), BT AT = AT]

                 = AT                   [From (1), BT AT = AT]

Hence, AT is idempotent.

Similarly, it can be proved that BT is idempotent.

Ask the Expert