In this note we use elementary facts from 3-dimensional linear algebra to demonstrate the formula for area changes under arbitrary linear maps A : R³ -> R³. We do it in general, from a hint given by the well known invertible case, which is an important result used in continuum mechanics. An intrinsic formula for the case when rank A = 2 is obtained and we finish by showing that we are really exploring a property of the cofactor matrix of A for an orthonormal basis.
Cofactor matrix; linear algebra
