Question

If \(A=\left(\begin{array}{ccc}5 & 5 x & x \\ 0 & x & 5 x \\ 0 & 0 & 5\end{array}\right)\) and \(\left|A^{2}\right|=25\), then \(|x|\) is equal to
(A) \(\frac{1}{5}\)
(B) 5
(C) \(5^{2}\)
(D) 1

Answer 1

Ans : (A)
Hint : \(\left|A^{2}\right|=|A|^{2}=25\)
$$
\Rightarrow(25 x)^{2}=25
$$
$$
\Rightarrow x=\frac{1}{5}
$$

Answer 2

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Answer 3

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