Let $X$ be a square matrix. Consider the following two statements on $X$. I. $X$ is invertible. II. Determinant of $X$ is non-zero. Which one of the following is TRUE?

From standard linear algebra (the Invertible Matrix Theorem):

• A square matrix $X$ of size $n \times n$ is invertible (non-singular) if and only if its determinant is non-zero ($\det(X) \neq 0$).

• Thus, Statement I implies Statement II, and Statement II implies Statement I.

Therefore, statements I and II are equivalent statements (D).