okay that didn't work too well.. let's try this again:
https://www.cut-the-knot.org/blue/Modulo.shtml
after the field applet, point 4:
'In multiplication tables, the last row is always a reverse of the first row.'
is true, but doesn't cover all the symmetries in the elements, it'should be
'In multiplication tables, where b is the base, n is the index, the row b - n is always a reverse of the row n.'