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.

When the tutor is closed, the solution steps displayed in the tutor are re-displayed in the worksheet, with annotations showing the operations applied. Note that this display only and is not a value which can be further manipulated from within the worksheet. The value returned from the tutor, which can be used (for example, by referencing its equation label), is the state of the problem at the time the tutor was closed.

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

$M≔⟨⟨1\,2\,0⟩\left|⟨2\,3\,2⟩\right|⟨0\,2\,1⟩⟩$

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

$M^{-1}$

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

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