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KVPY2011MathematicsDeterminants

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 such that A ^ k = I (the identity matrix) and B ^ =0 (the zero matrix). Then-

Options

  1. AA + B = I
  2. Bdet ( AB )=0
  3. Cdet ( A + B ) 0
  4. D( A + B )^ m =0 for some integer m

Correct answer

B. det ( AB )=0

Step-by-step solution

A^ k =I, B^ =0( det (B)=0) det (A B)=0

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