MCQ
If A is a non-singular matrix, then
- A$| A | \neq\left| A ^{\prime}\right|$
- B$\left| AA ^{\prime}\right| \neq\left| A ^2\right|$
- ✓$| A |+\left| A ^{\prime}\right| \neq 0$
- D$\left| A ^{-1}\right| \neq| A |^{-1}$
✓
Answer
Correct option: C.
$| A |+\left| A ^{\prime}\right| \neq 0$
(c) $| A |+\left| A ^{\prime}\right| \neq 0$
Explanation: $\because| A | \neq 0$ and $| A |=\left| A ^{\prime}\right|$.
So, $|A|+\left|A^{\prime}\right|=|A|+|A|=2|A| \neq 0$.
$\therefore$ Option (d) is the correct answer.
Explanation: $\because| A | \neq 0$ and $| A |=\left| A ^{\prime}\right|$.
So, $|A|+\left|A^{\prime}\right|=|A|+|A|=2|A| \neq 0$.
$\therefore$ Option (d) is the correct answer.
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