If $A =\begin{bmatrix}α&0\\1&1\end{bmatrix}$ and $B = \begin{bmatrix}1&0\\2&1\end{bmatrix}$, then the value of $α$ for $A^2=B$.

1

We have,

$A^2=B⇒\begin{bmatrix}α&0\\1&1\end{bmatrix}\begin{bmatrix}α&0\\1&1\end{bmatrix}=\begin{bmatrix}1&0\\2&1\end{bmatrix}$

$⇒\begin{bmatrix}α^2&0\\1+α&1\end{bmatrix}=\begin{bmatrix}1&0\\2&1\end{bmatrix}$

On comparison

$⇒α^2=1$ and $α+1=2$

$⇒α=1$