I wrote this script for verifying my matrix calculations I did for my studies. Internally, it works with fractions (even when you enter rational numbers), so the results are exact (modulo your own rounding errors at input). Output of rational numbers will take place with up to 16 digits after the decimal point.
You may enter rational numbers (i.e. 0.3333, 0.78 etc.) or fractions (i.e. 1/4, 3/7 etc.). You must separate the numbers with spaces, so the numbers itself must not contain spaces. Every line you enter represents a row in the matrix.