Matrix Transformation of R^2 Via Column Vectors

This app shows the effect of multiplying a ${\mathrm{R}}^2ℝ^2$ matrix $MM$ with the unit vectors $e_1(1,0)e\_1\; (1,0)$ and $e_2(0,1)e\_2\; (0,1)$ to get matrices $M{e}_{1}Me\_1$ and $M{e}_{2}Me\_2$. This is shown by displaying the initial and resulting matrices and their vectors drawn a unit grid.