Answer
See below.
Work Step by Step
We multiply the matrices as follows:
$AB=\left[\begin{array}{c c} 4\cdot2+1\cdot(-7)& 4\cdot(-1)+1\cdot4\\ 7\cdot2+2\cdot(-7)& 7\cdot(-1)+2\cdot4\end{array} \right]=\left[\begin{array}{c c} 1& 0\\ 0& 1\end{array} \right]$
$BA=\left[\begin{array}{c c} 2\cdot4+(-1)\cdot7& 2\cdot1+(-1)\cdot2\\ (-7)\cdot4+4\cdot7& (-7)\cdot1+4\cdot2\end{array} \right]=\left[\begin{array}{c c} 1& 0\\ 0& 1\end{array} \right]$
Hence we verified what we had to.
