Determinant Calculator

Calculate the determinant of 2x2 and 3x3 matrices with step-by-step solutions.

Matrix Determinant

How to Use

1. Select Matrix Size
Choose between 2×2 or 3×3 matrix
2. Enter Elements
Fill in the matrix values row by row
3. Calculate
Get the determinant with step-by-step solution

Quick Examples

2×2 Identity Matrix
[[1,0],[0,1]] → det = 1
2×2 Example
[[2,3],[1,4]] → det = 5
3×3 Identity Matrix
[[1,0,0],[0,1,0],[0,0,1]] → det = 1

About Matrix Determinants

The determinant is a scalar value that can be computed from the elements of a square matrix. It provides important information about the matrix, such as whether it's invertible.

2×2 Matrix Formula

det = ad - bc
For matrix [[a,b],[c,d]]

3×3 Matrix Formula

det = a(ei - fh) - b(di - fg) + c(dh - eg)
For matrix [[a,b,c],[d,e,f],[g,h,i]]

Properties

det = 0

Matrix is singular (not invertible)

det ≠ 0

Matrix is non-singular (invertible)

Identity Matrix

det = 1 for any size identity matrix

Zero Matrix

det = 0 for any size zero matrix