He is mostly talking about computational linear algebra problems of a large scale type due to large matrices: the "computational intensity" comes from having really large matrices (kxk for k = 100's, 1 000's, 10 000's, 100 000's, 1 000 000's, ...).

In computer graphics, the situation is often different. Usually, you have small matrices (kxk for k=2,3,4); a huge number of vectors; and you want to apply your matrix to all of those vectors. Very often, these matrices have very well known forms and also known well behaved inverses. There isn't really a significant computational cost in computing the inverse (you'll very often write down its formula by hand), and conditioning is usually not an issue (consider a rotation matrix for example or undoing translations with homogeneous coordinates).

Thank you for the clarification. I didn't realize we were talking about that kind of scale.

You may need an inverse, but you shouldn’t call .inverse() or inverse(A).

Since transformation matrices have simple structure, you can invert them much much faster.

Ex: inverse(R, u) is (R^T, -R^T * u)