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ISI 2017 MMA 20

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The number of the ordered pair (X, Y), where X and Y are N*N real matrices such that XY-YX=​​​​​​​​​​​​​​ I is

A) 0

B) 1

C) N

D) Infinite
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Lets check it for 1*1 matrix.

For 1*1 matrix we have XY=YX

So, XY-YX =0

So, for 1*1 matrices there does not exist any matrix X and Y such that XY-YX = 1 (the identity matrix for 1*1 matrices)

So,the answer is 0 which is option A.

Hence option A is the correct answer.
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