Matrices and Determinants: JEE Main 2022 Mathematics question

Let $A=\left[\begin{array}{cc}1 & -1 \\ 2 & \alpha\end{array}\right]$ and $B=\left[\begin{array}{cc}\beta & 1 \\ 1 & 0\end{array}\right], \alpha, \beta \in \mathbf{R}$. Let $\alpha_{1}$ be the value of $\alpha$ which satisfies $(\mathrm{A}+\mathrm{B})^{2}=\mathrm{A}^{2}+\left[\begin{array}{ll}2 & 2 \\ 2 & 2\end{array}\right]$ and $\alpha_{2}$ be the value of $\alpha$ which satisfies $(\mathrm{A}+\mathrm{B})^{2}=\mathrm{B}^{2}$. Then $\left|\alpha_{1}-\alpha_{2}\right|$ is equal to ___________.