Better I think would be to say "the result in column i and row j is the sum of product of elements in column i of the left cracovian and column j of the right cracovian".

And even by this definition the example given doesn't seem to track (and the strangeness of sometimes saying "+" and sometimes not, and having both "0" and "-0" in the example is bananas!):

   {  3  2 } {  1  -4 }  =   {  5   -2 }
   { -1  0 } { -2   3 }  =   {  0    2 }


   3 * 1 + -1 * -2 == 5 -- check
   3 * -4 + -1 * 3 == -15 -- what?
   2 * 1 + 0 * -2 == 2 (okay, but shouldn't this be in the lower left, column 1 dotted with column 2?)
   2 * -4 + 0 * 3 = -8 (now I'm really missing something)