Order of Multiplication for Symmetry Tables describing Geometric Shapes

I am construction multiplication tables for the symmetries of various geometric figures and I find myself wondering if there is a standardised order in which the tables are meant to be read?

__ | __D__ |_ F^2_ |

r __|__ |_ #_ |

r^2|___ |___ |

(The values D, F^2,... are meaningless so ignore them.)

My question is which goes first, the row or the column operation? Is the position denoted by # in the table above r*F^2 = # or F^2*r = #. Or is the order table specific? (This seems unlikely.)

The PDF I'm using implies (Row*Column; or a left to right bias as when reading english) but doesn't explicitly say that. I am just looking for confirmation of that though.

Sorry for the super simple question. I did a search and it only returned things that looked unrelated.