88 - The Jacobian
Matrices transform coordinates, and this is exactly it. The Jacobian Matrix is used to represent how a function transforms the coordinate grid around a certain point. If a normal matrix has columns which each represent the transformation to that unit vector, the columns of the jacobina have the partial derivatives of that function with each column representing each variable.
This matrix has a determinant, of course. This will denote how much it scales, shrinks out or stretches an unit square/cube. Whenever we do integration in multivariate calculus that involve changing coordinate systems we will need to multiply the function by the determinant of the jacobian for that respective system.