Matrix Determinant

All math tools

Calculate the determinant of 2x2 and 3x3 square matrices.

Matrix Size

Matrix Elements

Matrix A =

000

Determinant Result

det(A)

Matrix TypeSingular (Non-invertible)

Inversion HintNo distinct solution

About this calculator

What is a Determinant?

The determinant is a scalar value that can be computed from the elements of a square matrix. It encodes important properties of the linear transformation described by the matrix. If the determinant is zero, the matrix is singular (not invertible) and the transformation squashes the space into a lower dimension.

💡

Pro Tips

If det(A) = 0, the system of equations has either no solution or infinitely many solutions.
The absolute value of the determinant represents the area (in 2D) or volume (in 3D) scaling factor.
det(AB) = det(A) * det(B).

Fun Facts

"The term 'determinant' was first used in the modern sense by Cauchy in 1812."
"In physics, determinants are used to calculate the Jacobian, which is essential for change of variables in integrals."
"Determinants can determine if a set of vectors is linearly independent."

Formula: det(A) = ad - bc (for 2x2)