Find the Determinant and Inverse Matrix
(a) Find the determinant for A by calculating the elementary products.
(b) Find the determinant for A by reducing the matrix to upper triangular form.
(c) Use a cofactor expansion to calculate the determinant for A.
(d) Find the inverse matrix A^{-1} by using the adjugate matrix.
(e) Use elementary row operations to find the inverse matrix A^{-1}.