if AB = A and BA = B, then...

if AB = A and BA = B, then

A

`A^(2) B=A^(2)`

B

`B^(2) A = B^(2)`

C

`ABA=A`

D

`BAB=B`

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The correct Answer is:

A, B, C, D

We have , `A^(2) B = A ( AB) = A cdot A = A^(2) `,
` B^(2) A = B(BA) = BB = B^(2)`
ABA = A ( BA) = AB = A, BAB = B(AB) = BA = B`

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