Which of the following statements are true with respect to Linear Algebra?
A) A matrix is invertible if and only if its determinant is non-zero.
B) Eigenvalues and eigenvectors are defined for matrices only in square form.
C) A vector space is defined over a field, meaning its operations (addition and scalar multiplication) are defined with respect to the field's rules.
D) A diagonal matrix has only non-zero entries on the diagonal, and all off-diagonal entries are zero.