Matrices and Determinants 2 Question 19
21. 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 $C$
(1981, 2M)
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Answer:
Correct Answer: 21. (b)
Solution:
- 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 as many elements as $C$.
