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3 and 4 .Determinants and Matrices
easy
यदि $A = \left[ {\begin{array}{*{20}{c}}\alpha &2\\2&\alpha\end{array}} \right]$ और $|{A^3}|$=125, तो $\alpha = $
A
$ \pm $ $3$
B
$ \pm $ $2$
C
$ \pm $ $5$
D
$0$
(IIT-2004)
Solution
(a) $|{A^3}| = 125$; $|A{|^3} = 125 = {5^3}$ $ \Rightarrow $ $|A| = 5$ $ \Rightarrow $ ${\alpha ^2} – 4 = 5 \Rightarrow \alpha = \pm 3$.
Standard 12
Mathematics