Matrix Calculator
Calculate the determinant, inverse, and matrix multiplication for 2×2 and 3×3 matrices. Includes trace and step-by-step results.
Determinant
—
Result Matrix —
Trace (sum of diagonal) —
How to Use This Calculator
Select Matrix Size (2×2 or 3×3) and Operation (determinant, inverse, or multiply). Enter the matrix A values (and matrix B for multiplication). Results appear instantly.
Formula
2×2 det = ad−bc • Inverse = (1/det)×adj(A) • (A×B)ᵢⱼ = Σ Aᵢₖ×Bₖⱼ
Example
[[1,2],[3,4]]: det=−2, Inverse=[[−2,1],[1.5,−0.5]], Trace=5
Frequently Asked Questions
- The determinant is a scalar value that can be computed from a square matrix. For a 2×2 matrix [[a,b],[c,d]], det = ad−bc.
- A zero determinant means the matrix is singular — it has no inverse, and its rows/columns are linearly dependent.
- For [[a,b],[c,d]] with det=ad−bc≠0: inverse = (1/det)×[[d,−b],[−c,a]].
- For 2×2 matrices A and B, the product C=A×B is computed as cᵢⱼ = sum of row i of A times column j of B.
- The trace is the sum of diagonal elements. For [[1,2],[3,4]], trace = 1+4 = 5.