Ordinary, min-plus, and max-plus — one product, three meanings
Every entry of a matrix product reduces a row-against-column list of candidates. The arithmetic decides what "reduce" means: blend them all, or pick one.
Row of A / column of B feeding the selected product entry.
Selected product cell; in tropical modes, also the winning candidate k.
Greyed entries are the additive identity of the active semiring — the "no contribution" element: 0 for ordinary, +∞ for min-plus, −∞ for max-plus.