$A=\left(\begin{array}{cccc}{a}_{11}& {a}_{12}& \dots & {a}_{1N}\\ {a}_{21}& {a}_{22}& \dots & {a}_{2N}\\ & \vdots \\ {a}_{N1}& {a}_{N2}& \dots & {a}_{NN}\end{array}\right)$

The computer does not verify the invertibility or the conditioning of the matrix. A valid result is when the last computation step is the identity matrix is on the left. Otherwise, can possibly be produced by interchanging rows or columns solvability.