Dimension of Algebraic Dual

Theorem
Let $$G$$ be an $n$-dimensional $R$-module.

Let $$G^*$$ be the algebraic dual of $$G$$.

Let $$G^{**}$$ be the algebraic dual of $$G^*$$.

Then $$G^*$$ and $$G^{**}$$ are also $n$-dimensional.

Proof
Follows directly from Product of Linear Transformations.