If A = [ 2 2 ] and | A 3 | = 125 , then the value of is [2004]

Question

If $A = [\begin{matrix} α & 2 \\ 2 & α \end{matrix}]$ and $| A^{3} |$ $= 125,$ then the value of $α$ is [2004]

Smart Achievers · Accepted Answer

(3)

$A = [\begin{matrix} α & 2 \\ 2 & α \end{matrix}]$ and $| A^{3} |$ $= 125$ $α$ $| A^{3} |$ $= 125$

$∴$ $| A |$ $= α^{2} - 4$

Now, $| A |^{3}$ $= 125$

$\Rightarrow {(α^{2} - 4)}^{3} = 125 = 5^{3}$

$\Rightarrow α^{2} - 4 = 5$

$\Rightarrow α = \pm 3$

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