If AB = A and BA = B then

Engineering

Mathematics

Introduction to Matrix

Algebra of Matrices

Multiplication of Matrices

Question

If AB = A and BA = B then

A²B = A²

B²A = B²

ABA = A

BAB = B

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We have, AB = A and BA = B

Now, checking each option:

Option A : A²B = A(AB) = AA = A²

Option B : B²A = B(BA) = BB = B²

Option C : ABA = A(BA) = AB = A and

Option D : BAB = B(AB) = BA = B.

Hence, all options are correct.