Matrix Calculator
Perform matrix operations including addition, subtraction, multiplication, determinant, inverse, and transpose on matrices up to 4×4. Essential for linear algebra, engineering, physics, and computer graphics.
| Operation | Requirement |
|---|---|
| A + B / A − B | A and B must have the same dimensions |
| A × B | Columns of A must equal rows of B |
| det(A) | A must be square (n × n) |
| A⁻¹ | Square matrix and det(A) ≠ 0 |
| Aᵀ | Any matrix — dimensions become m×n → n×m |
Choose the operation from the button row at the top. Operations marked with A and B (add, subtract, multiply) require two matrices. Det, inverse, and transpose only use Matrix A.
Click 2×2, 3×3, or 4×4 to resize the matrix. All cells reset to 0 when resized. For multiplication, the number of columns in A must equal the number of rows in B.
Only defined for square matrices. A non-zero determinant means the matrix is invertible. If det = 0, the matrix is singular and has no inverse.
The inverse A⁻¹ satisfies A × A⁻¹ = I (identity matrix). Only exists when the determinant is non-zero. Used to solve systems of linear equations.
- •Matrix multiplication is not commutative: A×B ≠ B×A in general.
- •For a 2×2 matrix [a,b;c,d], det = ad − bc.
- •To solve Ax = b for x, compute x = A⁻¹ × b using the inverse operation.