Consider the set A of all determinants of order 3 with entries 0 or 1 only. Let B be the subset of A consisting of all determinants with value 1, and let C be the subset of A consisting of all determinants with value -1. Then

JEE Main Mathematics question

Consider the set of all determinants of order 3 with entries 0 or 1 only. Let be the subset of consisting of all determinants with value 1, and let be the subset of consisting of all determinants with value . Then

(A) is empty
(B) has as many elements as Correct
(C)
(D) has twice as many elements as

Answer: (B)

Solution

Interchanging the first two rows changes the sign of a determinant, giving a one-one correspondence

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Question ID VK-003165