If A=[α255−α] and detA10=1024, then α

A=[α255−α]A10=1024⇒A10=210⇒A=2⇒−α3−25=2⇒−α3=27⇒α3=−27=−33α=−3

If A=[α255−α] and detA10=1024, then α

A=[α255−α]A10=1024⇒A10=210⇒A=2⇒−α3−25=2⇒−α3=27⇒α3=−27=−33α=−3

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If $A = [\begin{array}{cc} α^{2} & 5 \\ 5 & - α \end{array}]$ and $\det (A^{10}) = 1024$ , then $α$

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Detailed Solution

$A = [\begin{array}{cc} α^{2} & 5 \\ 5 & - α \end{array}]$

$|A^{10}| = 1024$

$\Rightarrow {|A|}^{10} = 2^{10}$

$\Rightarrow |A| = 2$

$\Rightarrow - α^{3} - 25 = 2$

$\Rightarrow - α^{3} = 27$

$\begin{array}{l} \Rightarrow α^{3} = - 27 = {(- 3)}^{3} \\ α = - 3 \end{array}$

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If $A = [\begin{array}{cc} α^{2} & 5 \\ 5 & - α \end{array}]$ and $\det (A^{10}) = 1024$ , then $α$