If A=a 01 1 and B=1 02 1, then the value of a for which A2=B, is

Solution:

We have,

$A^{2} = B$

$\begin{array}{l} = [\begin{array}{cc} a & 0 \\ 1 & 1 \end{array}] [\begin{array}{cc} a & 0 \\ 1 & 1 \end{array}] = [\begin{array}{ll} 1 & 0 \\ 2 & 1 \end{array}] \\ = [\begin{array}{cc} a^{2} & 0 \\ a + 1 & 1 \end{array}] = [\begin{array}{ll} 1 & 0 \\ 2 & 1 \end{array}] \end{array}$

$\Rightarrow a^{2} = 1$ and $a + 1 = 2 \Rightarrow a = \pm 1$ and $a = 1 \Rightarrow a = 1$

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