I claim that componentwise addition of scalars to
matrices is wrong.
By default, doallmxops=true.
Calculate ratsimp(m.m^^-1+m). This yields matrix
Now calculate subst(m,n,n.n^^-1+n). This yields matrix
([a+1,b+1],[c+1,d+1]). I believe this is wrong.
Note that this happens even when dotident is not equal
to 1. Only if dotexptsimp=false (which is a pretty radical
restriction) does the subst case match the non-subst
As far as I can tell, the only sensible thing for
scalar+matrix to mean is scalar*identitymatrix + matrix.
I do not believe that componentwise addition of scalar
to matrix is ever useful; if it is, you can always write it
as scalar*allonesmatrix + matrix.
Note that scalar/matrix *multiplication* is a completely
different matter -- componentwise is perfectly
meaningful and useful there.