Visualising linear transformations in R3

This applet shows the geometric effect of a linear transformation $T$ in $\mathbb R^3$.

You can type a 3×3 matrix $M$ on the right hand side of the applet, and then click Play to see how the vertices of a cube are transformed when multiplying by $M$.

Can you see if the corresponding transformations are injective, surjective, or invertible?

There is also an option to toggle the matrix to be 2×3 or 3×2. In the case of a 2×3 matrix, the image will be mapped to something completely flat, a subset of the $xy$-plane.

Other resources:

Geogebratube page for this applet