Show that there are no 2x2 matrices A and B such that $\displaystyle AB-BA=\begin{pmatrix}1 & 0\\0 & 1\end{pmatrix}$

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- Feb 10th 2009, 08:33 PMjennifer1004Matrix proof
Show that there are no 2x2 matrices A and B such that $\displaystyle AB-BA=\begin{pmatrix}1 & 0\\0 & 1\end{pmatrix}$

- Feb 10th 2009, 08:36 PMJhevon
let $\displaystyle A = \left( \begin{array}{cc} a_1 & a_2 \\ a_3 & a_4 \end{array} \right)$ and $\displaystyle B = \left( \begin{array}{cc} b_1 & b_2 \\ b_3 & b_4 \end{array} \right)$

compute $\displaystyle AB - BA$ and show that this can never be $\displaystyle \left( \begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array} \right)$ by equating corresponding entries