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 A consisting 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

The correct option is D B has twice as many elements as C

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 themself sign changes]
Given, C is the subset having determinant with value -1.
$\therefore$ B has many elements as C.