Learn How to Calculate Product of Determinants - Tutorial

Definition:

Product of determinants is the multiplication of determinants of two matrices.

Example 1 : 2 x 2 Matrix

Solution:

Step 1:

|A| = (4 x 6) - (2 x 7) |A| = 24 - 14 |A| = 10

Step 2:

|B| = (2 x 7) - (8 x 1) |B| = 14 - 8 |B| = 6

Step 3:

|A| x |B| = 10 x 6 = 60

Example 2 : 3 x 3 Matrix

Solution:

Step 1:

|A| = 5 x ((8 x 3) - (7 x 6)) - 2 x ((8 x 4) - (6 x 1)) + 7 x ((4 x 7) - (3 x 1)) |A| = 5 x (24 - 42) - 2 x (32 - 6) + 7 x (28 - 3) |A| = 5 x (-18) - 2 x 26 + 7 x 25 |A| = - 90 - 52 + 175 |A| = 33

Step 2:

|B| = 8 x ((9 x 6) - (7 x 4)) - 3 x ((2 x 6) - (5 x 7)) + 4 x ((2 x 4) - (9 x 5)) |B| = 8 x (54 - 28) - 3 x (12 - 35) + 4 x (8 - 45) |B| = 8 x 26 - 3 x (-23) + 4 x (-37) |B| = 208 + 69 - 148 |B| = 129

Step 3:

|A| x |B| = 33 x 129 = 4257