Let $A$ and $B$ be real matrices of the form $\left[\begin{array}{ll}\alpha & 0 \\ 0 & \beta\end{array}\right]$ and $\left[\begin{array}{ll}0 & \gamma \\ \delta & 0\end{array}\right]$, respectively. Statement 1: $AB - BA$ is always an invertible matrix. Statement 2: $AB - BA$ is never an identity matrix. (1) Statement 1 is true, Statement 2 is false. (2) Statement 1 is false, Statement 2 is true. (3) Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation of Statement 1. (4) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.
Let $A$ and $B$ be real matrices of the form $\left[\begin{array}{ll}\alpha & 0 \\ 0 & \beta\end{array}\right]$ and $\left[\begin{array}{ll}0 & \gamma \\ \delta & 0\end{array}\right]$, respectively.\\
Statement 1: $AB - BA$ is always an invertible matrix.\\
Statement 2: $AB - BA$ is never an identity matrix.\\
(1) Statement 1 is true, Statement 2 is false.\\
(2) Statement 1 is false, Statement 2 is true.\\
(3) Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation of Statement 1.\\
(4) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.