The Table of Multiplication is a teaching tool for new mathematics students.
As you can see on the Table of Multiplication here, the number of squares n the rectangle = the number symbol, i.e. 15 squares = 3 x 5 or 5 x 3.  5 x 3 of 3 x 5 are both giving 15 squares no matter which comes first.  This transmutation-ability is called the Commutative Law of Addition.
Note also that the numbers that are circled on this chart are all square numbers. You will see that each forms a square on the grid eg. 5 x 5 = 25 which s a square on this grid.
Students can see visually and explore the table by tracing the patterns with the finger, drawing the pattersn, moving through space in the patterns using objects or other symbols of the grid.
In any case, learning the able involves repetition for complete memorization.
T.E. Pelton, New World Education: Kinesiology of Math (c) 2012