Let A and B be real matrices of the form ![\left[\begin{array}{cc}\alpha&0\\0&\beta\end{array}\right]\ and\ \left[\begin{array}{cc}0&\gamma\\\delta&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Calpha%26amp%3B0%5C%5C0%26amp%3B%5Cbeta%5Cend%7Barray%7D%5Cright%5D%5C+and%5C+%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0%26amp%3B%5Cgamma%5C%5C%5Cdelta%26amp%3B0%5Cend%7Barray%7D%5Cright%5D "\left[\begin{array}{cc}\alpha&0\\0&\beta\end{array}\right]\ and\ \left[\begin{array}{cc}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.
(a) Statement 1 is true, Statement 2 is false.
(b) Statement 1 is false, Statement 2 is true.
(c) Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation of Statement 1.
(d) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.
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left[\begin{array}{cc}\alpha&0\\0&\beta\end{array}\right]\ and\ \left[\begin{array}{cc}0&\gamma\\\delta&0\end{array}\right][/tex], respectively.
Statement 1: AB – BA is always an invertible matrix.
Statement 2: AB – BA is never an identity matrix.
(a) Statement 1 is true, Statement 2 is false.
(b) Statement 1 is false, Statement 2 is true.
(c) Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation of Statement 1.
(d) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.
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