Determinant Calculator
determinant calculator. Get instant, accurate results. Enter values for instant results with step-by-step formulas.
Reviewed by Manoj Kumar, Mathematics Educator
Reviewed by Manoj Kumar, Mathematics Educator
Formula
2x2: det = ad - bc | 3x3: det = a(ei-fh) - b(di-fg) + c(dh-eg)
The determinant is a scalar value computed from a square matrix. For 2x2: ad-bc. For 3x3: cofactor expansion along the first row. Determinant = 0 means the matrix is singular (no inverse, zero volume).
Worked Examples
Example 1: 2x2 matrix
Problem:|1 2; 3 4|
Solution:det = (1)(4) - (2)(3) = 4 - 6 = -2
Result:det = -2
Example 2: 3x3 matrix with a zero determinant (singular)
Problem:|1 2 3; 4 5 6; 7 8 9|
Solution:det = 1(5×9-6×8) - 2(4×9-6×7) + 3(4×8-5×7) = 1(45-48) - 2(36-42) + 3(32-35) = -3 + 12 - 9 = 0
Result:det = 0 (singular matrix, no inverse — rows are linearly dependent)
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy