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Question

Let A and B be two matrices different from I such that AB=BA and AnBn is invertible for some natural number n. If AnBn=An+1Bn+1=An+2Bn+2, then
I. (IA) is singular
II. (IB) is singular
III. A+B=AB+I
IV. (IA)(IB) is non-singular

A
I, II, III, IV
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B
I, III, IV only
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C
I, II, III only
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D
I, II, IV only
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Solution

The correct option is D I, II, IV only
Since matrices A and B are commutative hence I, II, III are true.

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