How can I increase the size of a subpanel to fit the breaker for a solar array?
That is correct. The 100A breaker in the main panel protects the wiring to the subpanel, and the subpanel itself.   The "main" breaker in the subpanel is nothing but a shutoff switch (unless it is also a GFCI or something, as in the case of a hot tub panel).  

The subpanel must be large enough to be protected by either its own main breaker (if it even has one) or the supply breaker in the main panel.  In your case, a 60A subpanel would be wrong, but a 225A subpanel would be right.

The usual blunder people make is thinking the subpanel size must match the feed breaker, and thus they limit themselves to a panel with too few spaces. 

So go for broke. 42 spaces is not too many.  (Spaces are not circuits; a 40 “circuit" panel is often a 20-space). Good sign when spaces are a multiple of six, that indicates a panel of industrial quality (also sold in 3-phase).