In this article, the author expands the fact that a specific power of a nonsingular matrix is a unit matrix in a finite field based on a prime number, presented previously in the same named paper, into the singular situation, and proves that there is a subperiodic structure about a singular matrix in a finite field. An attempt is made to apply these characters to find out an accurate solution to indeterminate equations of linear algebra. These efforts prove to have the effect of solving the singularization occasionally occured in mapping from real number field into finite field, and provide an exact method for adoption in some problems of numerical calculation.