If k>I, and the determinant of the matrix A2 , where A = kkaa0aka00k, is k2 then a =

$$A=kkaa0aka00k=k2a$$ $$A2=k4a2=k2$$⇒$$a2=1k2$$ ∴$$a=1k$$

Q.

If k>I, and the determinant of the matrix A² , where A = $[\begin{matrix} k & k a & a \\ 0 & a & k a \\ 0 & 0 & k \end{matrix}]$ , is k²then $|\begin{matrix} a \end{matrix}| =$

Moderate

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$\frac{1}{k^{2}}$

$k^{2}$

$\frac{1}{k}$

answer is D.

(Detailed Solution Below)

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Detailed Solution

$|A| = |\begin{matrix} k & k a & a \\ 0 & a & k a \\ 0 & 0 & k \end{matrix}| = k^{2} a {|A|}^{2} = k^{4} a^{2} = k^{2} \Rightarrow a^{2} = \frac{1}{k^{2}} ∴ |a| = \frac{1}{k}$

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