Question

If A and B are two square matrices such that AB=A and BA=B,Then,
(i) A and B both are Idempotent matrix
(ii) Both are identity
(iii)Any one Idempotent matrix
(iv)Any one identity.

Answer 1

if A is idempotent then A*A=A

Answer 2

I know that

Answer 3

so if AB=A and BA = B then in order to be idempotent, A = B. But that's not explicitly stated nor can it be implied from the given info.

Answer 4

Both are identity matrix,hence obviously Idempotent matrix too.

Answer 5

yes but A = I => A is idempotent, but A is idempotent does not imply A is the identity matrix.

how about this

\[A ^{-1}AB=A ^{-1}A => B = I\]
so long as A & B are invertible

Answer 6

I get answer to most of the questions I ask immediately after I post them,even before anyone posts a solution many times :P

Answer 7

yep,inverse isn't true