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Let $A =\begin{bmatrix}5&5α&α\\0&α&5α\\0&0&5\end{bmatrix}$. If $|A^2| = 25$, then $|α|$ equals |
$\frac{1}{5}$ 5 $5^2$ 1 |
$\frac{1}{5}$ |
We have, $|A|=5× α × 5 = 25α$ [∵ A is an upper triangular matrix] Now, $|A^2| = 25$ $⇒|A|^2 = 25 ⇒(25α)^2=25⇒α^2=\frac{1}{25}⇒|α|=\frac{1}{5}$ |
