The Diagram Shows the Roads Connecting Four Cities $\mathrm{A}^{3}$ What Information Is Given by the Entry in Row

The diagram shows the roads connecting four cities.
The matrix A below represents the number of routes between each pair of cities without passing through another city.

Calculate $\mathrm{A}^{3}$ . What information is given by the entry in row 2 , column 3 of $\mathrm{A}^{3}$ ?

A) There are 4 ways to travel between cities $X$ and $Y$ by passing through one city
B) There are 5 ways to travel between cities $X$ and $Y$ by passing through exactly three cities
C) There are 4 ways to travel between cities $X$ and $Y$ by passing through at most two cities
D) There are 5 ways to travel between cities $X$ and $Y$ by passing through exactly two cities