First of all, make sure that you really want this. While inverse and determinant are fundamental mathematical concepts, in numerical linear algebra they are not as popular as in pure mathematics. Inverse computations are often advantageously replaced by solve() operations, and the determinant is often not a good way of checking if a matrix is invertible.
However, for very small matrices, the above is not true, and inverse and determinant can be very useful.
While certain decompositions, such as PartialPivLU and FullPivLU, offer inverse() and determinant() methods, you can also call inverse() and determinant() directly on a matrix. If your matrix is of a very small fixed size (at most 4x4) this allows Eigen to avoid performing a LU decomposition, and instead use formulas that are more efficient on such small matrices.
https://eigen.tuxfamily.org/dox/group__TutorialLinearAlgebra.html
Computing inverse and determinant