Let A, B be two square matrices such that A + B = AB, then(A) AB = BA� – InterviewSolution

InterviewSolution

1.

Let A, B be two square matrices such that A + B = AB, then(A) AB = BA (B) AB = -BA (C) AB + 2BA = 0 (D) None of these

Answer»

Answer is (A)

A + B = AB A + B – AB = 0

A + B – AB + I = 0+1

(A – I)(B – I) = 1

⇒ A -1 inverse of B -1

(B -1) (A -1) = I

BA – B – A + = I

BA – (B + A)

⇒ BA = B + A

= A + B

∴ AB = BA

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