Show Path with Arrows in a Matrix

Easily style vertices, edges, and their labels, and apply interesting functions. For a small increase in code sophistication, you gain quite an advantage.

    
Define a path:
Define the edge shape function:
Create the path graph:
Create the overall grid:
Overlay them:
A different approach uses GridGraph with the GraphHighlight option:
Highlight the path:
Add arrows to indicate the path direction: