The InverseTutor(M) command allows you to interactively find the inverse, if it exists, of the square Matrix M by using row operations to reduce the augmented Matrix $⟨M\|\mathrm{Id}⟩$ to $⟨\mathrm{Id}\|\frac{1}{M}⟩$ where Id is the identity Matrix of the same dimension as M. It returns the inverse Matrix.

Floating-point numbers in M are converted to rationals before computation begins.

The dimensions of the Matrix must be no greater than 5x5.

$\mathrm{with}\left(\mathrm{Student}\[\mathrm{LinearAlgebra}\]\right)\:$

$M≔⟨⟨1\,2\,0⟩\|⟨2\,3\,2⟩\|⟨0\,2\,1⟩⟩$

$M≔\left[\begin{array}{rrr}1& 2& 0\\ 2& 3& 2\\ 0& 2& 1\end{array}\right]$

$M^{-1}$

$\left[\begin{array}{ccc}\frac{1}{5}& \frac{2}{5}& -\frac{4}{5}\\ \frac{2}{5}& -\frac{1}{5}& \frac{2}{5}\\ -\frac{4}{5}& \frac{2}{5}& \frac{1}{5}\end{array}\right]$

$\mathrm{InverseTutor}\left(M\right)$