Matrix Determinant Calculator
Calculate the determinant of a 2×2 matrix.
Inputs
Determinant
-14.000000
Step by step
det = a×d − b×c
3×6 − 8×4
= -14.000000
Singular?
det ≈ 0?
= No
How it works
The determinant of a square matrix is a scalar value that indicates whether the matrix is invertible (non-zero determinant) and represents the signed volume scaling factor of the linear transformation. For a 2×2 matrix [[a,b],[c,d]], det = ad − bc.
Formula
2×2 Determinant
det([[a,b],[c,d]]) = a*d - b*c
- a,b,c,d
- Elements of the 2×2 matrix
Frequently Asked Questions
What does a zero determinant mean?
A zero determinant means the matrix is singular (non-invertible) and the transformation it represents collapses at least one dimension — the rows or columns are linearly dependent.
How is the determinant used in ML?
Determinants appear in Gaussian distributions (normalization constant involves det of covariance matrix), in checking rank of feature matrices, and in volume-preserving normalizing flows.