MCQ
જો $A=\left[\begin{array}{cc}\alpha^2 & 5 \\ 5 & -\alpha\end{array}\right]$ અને $\left|A^{10}\right|=1024$ હોય, તો $\alpha=\ldots \ldots \ldots$
- A$2$
- B$-2$
- C$3$
- ✓$-3$
$\left| {{A^{10}}} \right| = 1024$
$\therefore$ $\left| {{A^{10}}} \right| = {2^{10}}$
$\therefore$ $\left| A \right| = 2$
$\therefore$ $\left| {\begin{array}{*{20}{c}}{{\alpha ^2}}&5\\5&{ - \alpha }\end{array}} \right| = 2$
$\therefore$ $ - {\alpha ^3} - 25 = 2$
$\therefore$ ${\alpha ^3} = - 27$
$\therefore$ ${\alpha ^3} = - 3$
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