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? A. I implies II; II does not imply I B. II implies I; I does not imply II C. I and II are equivalent statements D. I does not imply II; II does not imply I

The correct answer is: A. I implies II; II does not imply I.

A square matrix is invertible if it has an inverse. The inverse of a matrix is another matrix that, when multiplied by the original matrix, gives the identity matrix. The determinant of a matrix is a number that is associated with the matrix. The determinant of a square matrix can be used to determine whether the matrix is invertible. A square matrix is invertible if and only if its determinant is non-zero.

Therefore, statement I implies statement II. However, statement II does not imply statement I. A matrix can have a non-zero determinant but not be invertible. For example, the matrix $\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ has a determinant of 1, but it is not invertible because it is a diagonal matrix.

In conclusion, statement I implies statement II, but statement II does not imply statement I. Therefore, the correct answer is A.