If C and D are two n × n non-singular matrices over the set of real number R such that C D=-D C , then n is

Correct answer: (C) n even integer. Given, C and D are non-singular matrix of order n ∵ |C| ≠ 0,|D| ≠ 0 C D=-D C |C D|=|-D C| |C||D|=(-1)^n|D||C| l=(-1)^n ∴ n is even integer.

Q46 / 160 · TS EAMCET 2020 (10 Sep Shift 2) · Mathematics

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
Correct answer
C
$n$ even integer
D
equal to one

Solution

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.

Hence, the correct answer is option: 'C'.

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

Solution

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