Question
Question: If A and B are two matrices such that AB = B and BA = A, then...
If A and B are two matrices such that AB = B and BA = A, then
A
(A5 – B5)3 = A – B
B
(A5 – B5)3 = A3 – B3
C
A – B is idempotent
D
A – B is nilpotent
Answer
A – B is nilpotent
Explanation
Solution
Since AB = B and BA = A
\ A and B both are idempotent
(A – B)2 = A2 – AB – BA + B2 = A – B – A + B = 0
\A – B is nilpotent