TS EAMCET · Maths · Determinants
If \(C\) and \(D\) are two \(n \times n\) non-singular matrices over the set of real number \(\mathbf{R}\) such that \(C D=-D C\), then \(n\) is
- A a natural number of the form \(3 k+5, k \in N\)
- B an odd integer
- C \(n\) even integer
- D equal to one
Answer & Solution
Correct Answer
(C) \(n\) even integer
Step-by-step Solution
Detailed explanation
Given, \(C\) and \(D\) are non-singular matrix of order \(n\) \(\because \quad|C| \neq 0,|D| \neq 0\) \(C D=-D C\) \(|C D|=|-D C|\) \(|C||D|=(-1)^n|D||C|\) \(\mathrm{l}=(-1)^n\) \(\therefore n\) is even integer.
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