Let M and N be two 3 × 3 matrices such that MN = NM. Further, if M N^2 and M^2 = N^4, then

JEE Advanced 2014 Mathematics question

Let M and N be two 3 × 3 matrices such that MN = NM. Further, if and , then

Answer: (A),(B)

Since M and N commute, . If were invertible, multiplying on the right by its inverse would give , contradicting . So is singular, and $ + = M·(M +

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Question ID VK-026284