Final answer:
A system AX = B has a unique solution when the matrix A is invertible, meaning its determinant is non-zero. Values of a and b that result in a non-zero determinant indicate the existence of a unique solution to the system.
Step-by-step explanation:
For a system of linear algebraic equations AX = B, a unique solution exists if the matrix A is invertible. This means that the determinant of matrix A must not be zero. When a and b are elements of matrix A, we must look at how they influence the determinant of A. If a change in a or b causes the determinant to be non-zero, then for those values of a and b, the system will possess a unique solution.
For example, consider a 2x2 matrix where A represents coefficients in a system of equations. The determinant of this matrix would be found using the formula ad - bc, where a, b, c, and d are elements from the matrix. If this determinant is non-zero, it ensures the existence of a unique solution to the system.