  Knot colorings are one of the simplest ways to distinguish knots, dating back
to Reidemeister, and popularized by Fox. In this mostly expository article, we
discuss knot invariants like colorability, knot determinant and number of
colorings, and how these can be computed from either the coloring matrix or the
Goeritz matrix. We give an elementary approach to this equivalence, without
using any algebraic topology. We also compute knot determinant, nullity of
pretzel knots with arbitrarily many twist regions.
