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Consider the set A of all determinants o...

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 `uu` C

D

B has thrice as many elements as C

Text Solution

Verified by Experts

The correct Answer is:
B
determinant of B = 1
Let 'B' be identity matrix
So, `B=|{:(1,0,0),(0,1,0),(0,0,1):}|`
If we interchange any 2 rows, determinant will be -1
Let, `C=|{:(1,0,0),(0,1,0),(0,0,1):}|,|C|=-1`
Here, number of elements in B and C are equal.
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