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Question: Answered & Verified by Expert
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
MathematicsDeterminantsTS EAMCETTS EAMCET 2020 (10 Sep Shift 2)
Options:
  • 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
Solution:
2211 Upvotes Verified Answer
The correct answer is: $n$ even integer
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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