Chapter 3.1, Problem 16E

The expansion of a 3 × 3 determinant can be remembered by the following device. Write a second copy of the first two columns to the tight of the matrix, and compute the determinant by multiplying entries on six diagonals:

Add the downward diagonal products and subtract the up-ward products. Use this method to compute the determinants in Exercises 15–18. Warning: This trick does not generalize in any reasonable way to 4 × 4 or larger matrices.

16. $\left|\begin{array}{ccc}0& 3& 1\\ 4& -5& 0\\ 3& 4& 1\end{array}\right|$