AP EAMCET · Maths · Determinants
A is the set of all matrices of order 3 with entries 0 or 1 only. \(B\) is the subset of \(A\) consisting of all matrices with determinant value 1. If \(C\) is the subset of \(A\) consisting of all matrices with determinant value -1, then
- A \(A=B \cup C\)
- B C is empty
- C B and C contain the same number of elements
- D B has twice as many elements as C
Answer & Solution
Correct Answer
(C) B and C contain the same number of elements
Step-by-step Solution
Detailed explanation
\( \text{Let } M \in A \text{ such that } \det(M) = 1 \). Then \( M \in B \). \( \text{Swapping two rows of } M \text{ results in a new matrix } M' \in A \). \( \det(M') = - \det(M) = -1 \). Thus \( M' \in C \). \( \text{This establishes a bijection between the sets B and C} \).…
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