Matrix Calculator
Add, subtract, and multiply matrices. Calculate determinant and transpose for up to 3×3 matrices.
About this calculator
Add, subtract and multiply 2×2 and 3×3 matrices, and find the determinant and transpose of matrix A. Choose the size, fill in the cells and press Calculate. An Example button loads sample values.
Matrices appear in linear algebra, computer graphics, economics and engineering.
How to use it
- Choose the size (2×2 or 3×3) and the operation.
- Enter the cells of Matrix A and Matrix B.
- Press Calculate, or use Det(A) or Transpose(A).
Rules
Addition and subtraction work cell by cell. Multiplication: each entry of A × B is the dot product of a row of A with a column of B. The 2×2 determinant is ad − bc. The transpose swaps rows and columns. Matrix multiplication is not commutative: A × B is usually different from B × A.
Worked example
A = [[1, 2], [3, 4]], B = [[5, 6], [7, 8]]
| A + B | [[6, 8], [10, 12]] |
| A × B | [[19, 22], [43, 50]] |
| det(A) | 1×4 − 2×3 = −2 |
| Transpose of A | [[1, 3], [2, 4]] |
Tips and common mistakes
- You can multiply only if the columns of A equal the rows of B.
- If the determinant is zero the matrix has no inverse.
- Check your cells twice; one wrong sign changes the whole result.
- Use the transpose to switch row and column vectors.
- Try the Example button to see the layout.
Frequently asked questions
How do I multiply two matrices?
Take the dot product of each row of the first with each column of the second.
What is a determinant?
A single number that summarises a square matrix; zero means it is singular.
What is the transpose?
The matrix flipped over its diagonal.
Does the order matter in multiplication?
Yes, A × B generally differs from B × A.
Can I add matrices of different sizes?
No.
What sizes does the tool support?
2×2 and 3×3.