What is a Matrix Determinant?

The determinant is a scalar value that can be computed from the elements of a square matrix. It provides important information about the matrix, including whether it is invertible and the volume scaling factor of the linear transformation it represents.

How to Use This Calculator

Step 1: Select your matrix size (2×2, 3×3, 4×4, or 5×5)

Step 2: Enter the values for each element of your matrix

Step 3: Click “Calculate Determinant” to see the result and step-by-step solution

Determinant Formulas

2×2 Matrix:
det(A) = ad – bc

3×3 Matrix:
det(A) = a(ei – fh) – b(di – fg) + c(dh – eg)

Note: Larger matrices use expansion by minors (Laplace expansion) to calculate the determinant.