Question

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. Let C be the subset of the set of all determinants with value `-1`. Then
A. C is empty
B. B has as many elements as C
C. `A=B cup C`
D. B has twice as many elements as C

Answer 1

Since, A is the determinant of order 3 with entries 0 or 1 only.
Also, B is the subset of A consisting of all determinants with value 1.
[since, if we interchange any two rows or columns, then among themselves sign changes]
Given, C is the subset having determinant with value-1.
`therefore ` B has as many elements as C.