This paper focuses the knot insertion in the B-spline collocation matrix, with nonnegative determinants in all n x n sub-matrices. Further by relating the number of zeros in B-spline basis as well as changes (sign changes) in the sequence of its B-spline coefficients. From this relation, we obtained an accurate characterization when interpolation by B-splines correlates with the changes leads uniqueness and this ensures the optimal solution. Simultaneously we computed the knot insertion matrix and B-spline collocation matrix and its sub-matrices having nonnegative determinants. The totality of the knot insertion matrix and B-spline collocation matrix is demonstrated in the concluding section by using the input image and shows that these concepts are fit to apply and reduce the errors through mean square error and PSNR values