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Consider the set A of all matrices of order 3 3 with entries 0 or 1 only. Let B be the subset of A consisting of all matrices whose determinant is 1 . Let C be the subset of A consisting of all matrices whose determinant is -1 . Then which one of the following is correct?

Options

  1. AC is empty
  2. BB has as many elements as C
  3. CA = B C
  4. DB has thrice as many elements as C

Correct answer

B. B has as many elements as C

Step-by-step solution

determinant of B =1 Let ' B ' be identity matrix So, B= | array lll 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 array | If we interchange any 2 rows, determinant will be -1 Let, C = | array lll 1 & 0 & 0 0 & 0 & 1 0 & 1 & 0 array |,| C |=-1 Here, number of elements in B and C are equal.

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