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Just my 2 cent:
I know, that expression do not have to be evaluated but nevertheless
I would try to avoid the word "inverse()", because of lession #1: "Never
use matrix inversion".
x = b * A.adjoint().lu().invertor() (like benoit's solver())
But cleaner for me to read is, what Manoj suggesting:
x = solve(A,b); // left
x = solve(b,A); // right
x = solve(b, A.triangularView<Lower>()); // Gael's example
It's OK to read and understand w/o scarring about "inverse()" too.