Matrix Calculator
Work with square 2x2 or 3x3 matrices only. Choose determinant, add, subtract, multiply, or inverse. Type each row as numbers separated by spaces, and separate rows with semicolons. This is numeric linear algebra for small matrices, not a computer algebra system (CAS).
Rated 4.6 out of 5 based on 287 reviews
How to use the matrix calculator
- Choose the operation: determinant, add, subtract, multiply, or inverse.
- Enter matrix A as rows of numbers. Separate entries with spaces and rows with semicolons, for example 1 2; 3 4.
- For add, subtract, or multiply, enter matrix B the same way. Determinant and inverse use A only.
- Keep both matrices the same size (both 2x2 or both 3x3) when two matrices are required.
- Read the result rows. A singular matrix (determinant 0) has no inverse on this page.
Small-matrix arithmetic
2x2 and 3x3 determinant, sum, difference, product, and inverse
| Size limit | Square 2x2 or 3x3 only |
|---|---|
| Determinant | ad - bc for 2x2; cofactor expansion for 3x3 |
| Binary ops | Add, subtract, and multiply need matching sizes for A and B |
| Inverse | Exists only when the determinant is not zero |
| Input format | Rows joined by semicolons; cells separated by spaces or commas |
| Not a CAS | Numeric results only; no symbolic entries or larger dimensions |
What this matrix calculator covers
The page handles the five everyday jobs on tiny square matrices: determinant, entrywise add and subtract, matrix multiply, and inverse. Default A is 1 2; 3 4, whose determinant is -2.
Matrices, entries, and operations
A matrix here is a square grid of finite numbers. Entries must be numeric, not symbols. Determinant is a scalar. Add and subtract are entrywise. Multiply follows standard row-column products. Inverse is the unique square matrix that multiplies to the identity when it exists.
How parsing and math work
The engine splits on semicolons or newlines for rows, then on spaces or commas for cells. It demands two or three equal-length rows. Determinant uses ad - bc or a 3x3 cofactor expansion. Inverse divides the adjugate by the determinant and rejects near-zero determinants.
When a 2x2 or 3x3 tool is enough
Homework linear systems, 2D transforms, and quick singularity checks rarely need more than 3x3. Stay here for those cases instead of opening a full CAS.
Limits
Only 2x2 and 3x3. No 4x4, no rectangular multiply, no eigenvalues, no symbolic algebra. Singular matrices cannot be inverted. See the disclaimer.