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  4. If A=[α&0 1&1] and B [1&0 3&1] the value of α for which A2=B is

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Q. If $A=\begin{bmatrix}\alpha&0\\ 1&1\end{bmatrix}$ and $B \begin{bmatrix}1&0\\ 3&1\end{bmatrix} $the value of $\alpha$ for which $A^{2}=B$ is

Matrices

Solution:

We have $A^{2} \begin{bmatrix}\alpha&0\\ 1&1\end{bmatrix}\begin{bmatrix}\alpha&0\\ 1&1\end{bmatrix}=\begin{bmatrix}\alpha^{2}&0\\ \alpha+1&1\end{bmatrix}$
As $A^{2}=B,$ we get $\alpha^{2}=1$ and $\alpha+1=3 \Rightarrow \alpha=\pm 1$ and $\alpha=2 .$ This is not possible.