What is a determinant?

A scalar that represents the scaling factor of a linear transformation. For 2x2: det = ad-bc.

What does det=0 mean?

The matrix is singular (non-invertible). Rows/columns are linearly dependent.

How to compute 3x3 determinant?

Use the rule of Sarrus or expansion by minors: a(ei-fh) - b(di-fg) + c(dh-eg).

What are determinant properties?

det(AB)=det(A)*det(B), det(A^-1)=1/det(A), det(A^T)=det(A).

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Determinant Calculator

Compute the determinant for 2x2 and 3x3 matrices

Enter 2x2 Matrix

Determinant Formula

2x2: det = ad - bc

3x3: a(ei-fh) - b(di-fg) + c(dh-eg)

det(A) = 0 means singular matrix

det(AB) = det(A)*det(B)

The determinant measures how a matrix scales area/volume. A zero determinant means the transformation collapses space.

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