Algebra
Matrix determinant
A single number that tells you if a matrix is invertible — and how it scales area.
A single number that tells you whether a matrix is invertible — and how it scales area or volume.
Edit the matrix
A
→
det(A)
10
Non-zero ⇒ A is invertible.
What the determinant means
- |det| is the factor by which the matrix scales area (in 2D) or volume (in 3D).
- Sign of det tells you whether orientation is preserved (+) or flipped (−).
- det = 0 means space gets squashed onto a line or point — no inverse exists.
Your turn
Compute det[3 1; 2 4] and det[2 4; 1 2].
3×3 (cofactor expansion)
Expand along the top row, alternating signs + − +.
2×2 determinant
det = 0 means the rows are linearly dependent — the matrix squashes space flat.