An $n \times n$ matrix $A$ can be inverted by augmenting with an $n \times n$ identity matrix $I_{n}$, then using Gaussian elimination to convert the left-hand block to $I_{n}$.

The program randomly generates an $n \times n$ matrix with integer
entries. The outcomes of successive row operations are tabulated. Row
operations can be expressed in terms of rational numbers
(fractions). Multipliers may be input as fractions or decimals,
e.g., `-45/113` or `3.875`.

a new $n \times n$ matrix, $n = $ . | |

Add times row to row | |

Multiply row by | |

Exchange row and row |