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I just read in one of the questions answered by @MikeSpivey that the following table is provided in Sierksma's Linear and Integer Programming: Theory and Practice, Volume 1, page 144.

Primal Optimal Solution                     Dual Optimal Solution (a) Multiple                     implies    Degenerate (b) Unique and nondegenerate     implies    Unique and nondegenerate (c) Multiple and nondegenerate   implies    Unique and degenerate (d) Unique and degenerate        implies    Multiple 

I wonder if the information provided in this table is provided based on the assumption that matrix A has full rank.

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