If k>1, and the determinant of the matrix A², where $A = [\begin{array}{ccc} k & kα & α \\ 0 & α & kα \\ 0 & 0 & k \end{array}]$ , is k² then | $α$ | =

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$k^{2}$

$\frac{1}{k}$

$k$

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

answer is D.

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Detailed Solution

Given k>1 and
$\begin{array}{l} |A^{2}| = k^{2} \Rightarrow |A^{2}| = k^{2} \\ \Rightarrow {(k^{2} α)}^{2} = k^{2} \\ \Rightarrow α^{2} = \frac{1}{k^{2}} \Rightarrow | α | = \frac{1}{k} \end{array}$

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