If A- - 0- 0 1 - and B- 1 0- 0 1 - then the value of - for which A2-B is-

Given, A=[ α amp;0; nbsp; 0 amp;1 nbsp; ]and B=[ 1 amp;0; nbsp; 0 amp;1 nbsp; ] and A^2=B ⇒ A^2=[ α amp;0; nbsp; 0 amp;1 nb ...

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Byju's Answer

Standard IX

Mathematics

Null Matrix

If A=[ α 0; 0...

Question

If $A = [\begin{matrix} α & 0 0 & 1 \end{matrix}] and B = [\begin{matrix} 1 & 0 0 & 1 \end{matrix}]$ , then the value of $α$ for which $A^{2} = B$ is:

1

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2

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0

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No real values

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Solution

The correct option is A $1$
Given, $A = [\begin{matrix} α & 0 0 & 1 \end{matrix}]$ and $B = [\begin{matrix} 1 & 0 0 & 1 \end{matrix}]$ and $A^{2} = B$

$\Rightarrow A^{2} = [\begin{matrix} α & 0 0 & 1 \end{matrix}] [\begin{matrix} α & 0 0 & 1 \end{matrix}] = [\begin{matrix} α^{2} & 0 0 & 1 \end{matrix}] ∴ A^{2} = B$

$\Rightarrow [\begin{matrix} α^{2} & 0 0 & 1 \end{matrix}] = [\begin{matrix} 1 & 0 0 & 1 \end{matrix}]$
or,
$α^{2} = 1$
$∴ α = \pm 1$

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