Basketweave for 3 × 3 There is a shortcut for finding the determinant of a 3 × 3 matrix. F...

Basketweave for 3 × 3 There is a shortcut for finding the determinant of a 3 × 3 matrix. For example, let

,

and repeat the first and second columns to the right of the original three columns:

.

Now, add the products along the downward arrows and subtract the products along the upward arrows, getting

(10 + 0 + 4) − (16 + 0+ 10) = −12.

Show that the basketweave method does not generalize to finding determinants for higher-order matrices. Try a generalized basketweave method on

and show that it does not match the correct answer, which can be obtained by the cofactor method.