Matrix proof

Quote:

Originally Posted by jennifer1004

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

let $A = \left( \begin{array}{cc} a_1 & a_2 \\ a_3 & a_4 \end{array} \right)$ and $B = \left( \begin{array}{cc} b_1 & b_2 \\ b_3 & b_4 \end{array} \right)$

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