If A=α011 and B=1051 then the value of α for which A2 = B is

Given A=α011 and B=1 05 1 and A2=B⇒A2=α011α011=α20α+11Given A2=B⇒α20α+11=1051 or α2=1 and α+1=5 which is not possible at the sametime no real values of α.

If A=α011 and B=1051 then the value of α for which A2 = B is

Given A=α011 and B=1 05 1 and A2=B⇒A2=α011α011=α20α+11Given A2=B⇒α20α+11=1051 or α2=1 and α+1=5 which is not possible at the sametime no real values of α.

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If $A = [\begin{array}{cc} α & 0 \\ 1 & 1 \end{array}] and B = [\begin{array}{cc} 1 & 0 \\ 5 & 1 \end{array}]$ then the value of α for which A² = B is

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no real values

answer is D.

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Detailed Solution

Given $A = [\begin{array}{cc} α & 0 \\ 1 & 1 \end{array}] and B = [\begin{array}{ll} 1 0 \\ 5 1 \end{array}] and A^{2} = B$
$\begin{array}{l} \Rightarrow A^{2} = [\begin{array}{ll} α & 0 \\ 1 & 1 \end{array}] [\begin{array}{ll} α & 0 \\ 1 & 1 \end{array}] = [\begin{array}{cc} α^{2} & 0 \\ α + 1 & 1 \end{array}] \\ G i v e n A^{2} = B \\ \Rightarrow [\begin{array}{cc} α^{2} & 0 \\ α + 1 & 1 \end{array}] = [\begin{array}{ll} 1 & 0 \\ 5 & 1 \end{array}] or \end{array}$
$α^{2} = 1 and α + 1 = 5$ which is not possible at the same
time no real values of $α$ .