KVPY SB SX Exam 2011 Question Paper

Question : 81 of 120

Marks: +1, -0

Part-II MATHEMATICS

Let A and B be any two n × n matrices such that the following conditions hold: AB = BA and there exist positive integers k and

l

such that

A^k = I

(the identity matrix) and

B^l=0

(the zero matrix). Then

Solution:

A^k = I, Bl = 0

(det (B) = 0)
⇒ det (AB) = 0

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