NDA 2017 Mathematics question

Consider the set A of all matrices of order 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 . Then which one of the following is correct?

(A)C is empty
(B)B has as many elements as CCorrect
(C)
(D)B has thrice as many elements as C

Answer: (B)

Solution

Interchanging the first two rows of a matrix changes the sign of its determinant and keeps all entries 0 or 1. This operation is its own inverse, so it gives a one-to-one correspondence

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Question ID VK-028606