If $A$ and $B$ are two matrices such that $A+B$ and $AB$ are both defined, then

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

If $A = \left[ {\begin{array}{*{20}{c}}1&3&0\\{ – 1}&2&1\\0&0&2\end{array}} \right],B = \left[ {\begin{array}{*{20}{c}}2&3&4\\1&2&3\\{ – 1}&1&2\end{array}} \right]$, then $AB =$

Let $A$ and $B$ be real matrices of the form $\left[ {\begin{array}{*{20}{c}}
\alpha &0\\
0&\beta 
\end{array}} \right]$ and $\left[ {\begin{array}{*{20}{c}}
0&\gamma \\
\delta &0
\end{array}} \right]$, respectively

Statement $1$ : $AB – BA$ is always an invertible matrix

Statement $2$ : $AB -BA$ is never an identity matrix

If $A = \left[ {\begin{array}{*{20}{c}}2&5\\3&7\end{array}} \right]$and $B = \left[ {\begin{array}{*{20}{c}}0&3\\4&1\end{array}} \right],$then