If A=10−17,I=1001 and A2=8A+αI, then, the value of α is

A2=10−1710−17=10−8498A+αI=80−856+α00α=8+α0−856+α⇒8+α=1⇒+α=−7

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If $A = [\begin{array}{cc} 1 & 0 \\ - 1 & 7 \end{array}], I = [\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}] and A^{2} = 8 A + αI$ , then, the value of $α$ is

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answer is -7.

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Detailed Solution

$\begin{array}{l} A^{2} = [\begin{array}{cc} 1 & 0 \\ - 1 & 7 \end{array}] [\begin{array}{cc} 1 & 0 \\ - 1 & 7 \end{array}] = [\begin{array}{cc} 1 & 0 \\ - 8 & 49 \end{array}] \\ 8 A + αI = [\begin{array}{cc} 8 & 0 \\ - 8 & 56 \end{array}] + [\begin{array}{cc} α & 0 \\ 0 & α \end{array}] = [\begin{array}{cc} 8 + α & 0 \\ - 8 & 56 + α \end{array}] \\ \Rightarrow 8 + α = 1 \Rightarrow + α = - 7 \end{array}$