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.