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Question: Answered & Verified by Expert
Let $A$ be an $n \times n$ matrix. If det $(\lambda A)=\lambda^{s}$ det $(A)$, what is the value of $s ?$
MathematicsDeterminantsNDANDA 2010 (Phase 1)
Options:
  • A 0
  • B 1
  • C $-1$
  • D $n$
Solution:
1329 Upvotes Verified Answer
The correct answer is: $n$
We know, if $A$ is an $n \times n$ matrix, then
$\operatorname{det}(\lambda A)=\lambda^{s} \operatorname{det}(A)$
But given det $(\lambda A)=\lambda^{s} \operatorname{det} A$
$\Rightarrow s=n$

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