Consider the set A of all matrices of order 3 times 3 with entries 0 or 1 only Let B be the subset o...........

Mathematics (NDA) Set theory

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?

C is empty

B has as many elements as C

A=B∪C

D has thrice as many elements as C

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Explanation:

Given that 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. if C be the subset of A consisting of all matrices whose determinant is −1.
then By symmetry B has as many elements as C.