Arrhidaeus was the captain of the guard under Ptolemy Lagus.
The slave Susa brought him to the mines to investigate suspicious activity, but when Arrhidaeus found Barbara Wright, who resembled the queen, there, he had Susa killed. Arrhidaeus then brought Barbara and the First Doctor with him on his journey to Egypt with the dead body of Alexander the Great.
In an alternate timeline caused by Barbara becoming Ptolemy Lagus' queen, Arrhidaeus sided with Perdiccas in the struggle for the throne. He tried to assassinate Ptolemy Lagus, but was killed by him instead. (PROSE: The Book of Shadows)