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