Dror Bar-Natan: Classes: 2014-15: Math 1100 Algebra I:

Pensieve header: A progress monitor for JCF computations.

Dynamic[StringForm["`1` `5` `2` . `3` . `4`",
Sequence @@ (MatrixForm /@ {NN,PP,MM,QQ}),
If[Expand[NN]===Expand[PP.MM.QQ], "=", "≠"]
]]