Examples of determinants worked examples

det(A) = ad - bc
det(A) = (3 × 4) - (5 × 1)

det(A) = 12 - 5
det(A) = 7

The determinant of matrix A is 7.

Example 2: 3x3 Matrix

Consider the matrix:
B = [[1, 2, 3], [0, 4, 5], [1, 0, 6]]

det(B) = a(ei - fh) - b(di - fg) + c(dh - eg)
det(B) = 1 × ((4 × 6) - (5 × 0)) - 2 × ((0 × 6) - (5 × 1)) + 3 × ((0 × 0) - (4 × 1))

det(B) = 1 × (24 - 0) - 2 × (0 - 5) + 3 × (0 - 4)

det(B) = 1 × 24 - 2 × (-5) + 3 × (-4)
det(B) = 24 + 10 - 12

det(B) = 34 - 12
det(B) = 22

The determinant of matrix B is 22.