The determinant of a 3 × 3 matrix A is

The determinant of a 3 × 3 matrix A is defined as follows.

The determinant of a 3 × 3 matrix can also be found using the method of “diagonals.”

Step 1 Rewrite columns 1 and 2 of matrix A to the right of matrix A.

Step 2 Identify the diagonals d1 through d6 and multiply their elements.

Step 3 Find the sum of the products from d1, d2, and d3.

Step 4 Subtract the sum of the products from d4, d5, and d6 from that sum:

(d1 + d) + d3) – (d4 + d5 + d6).

Verify that this method produces the same results as the previous method given.

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