Typing every column of a matrix is not sufficiently general. Each element of the matrix can have its own type. While this is true, letting every matrix element

Typing every column of a matrix is not sufficiently general. Each element of the matrix can have its own type. While this is true, letting every matrix element have an arbitrary type is too general. The matrix' determinant should have a well defined type to be invertable. In your example mA/Pa * kg/V/s and mA/V * kg/V/s are compatible, so it works out.