Perform matrix operations including multiply, transpose, and inverse
Perform matrix operations without writing code or working through tedious row operations by hand. This calculator handles addition, subtraction, multiplication, scalar multiplication, matrix powers, transpose, determinant, trace, rank, inverse, reduced row echelon form, and eigenvalues for 2x2, 3x3, and 4x4 matrices.
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You need the determinant and inverse of a 2×2 matrix to solve a linear system by hand-check.
Matrix A
[ 1 2 ] [ 3 4 ]
Results
det(A) = (1·4 − 2·3) = −2
A⁻¹ = [ −2 1 ]
[ 1.5 −0.5 ]The determinant is non-zero (−2), so the matrix is invertible and the inverse is computed by the adjugate over the determinant. If the determinant were 0 the tool would report the matrix as singular rather than emit a bogus inverse, handling the edge case correctly.
Perform matrix operations without writing code or working through tedious row operations by hand. This calculator handles addition, subtraction, multiplication, scalar multiplication, matrix powers, transpose, determinant, trace, rank, inverse, reduced row echelon form, and eigenvalues for 2x2, 3x3, and 4x4 matrices.
Enter values into a grid, or fill a matrix instantly with the identity, zeros, ones, or random presets. The tool validates dimensions before binary operations - for example, it reports an error if you try to add matrices of different sizes. The determinant is computed by LU-style elimination with partial pivoting, the inverse via Gauss-Jordan elimination, and rank from the reduced row echelon form. Eigenvalues are found in closed form for 2x2 matrices and by solving the characteristic cubic (Cardano / trigonometric) for 3x3 matrices, with complex roots shown as conjugate pairs. Results are displayed in a clean grid or as a scalar/eigenvalue list.
Verify hand-calculated matrix operations - multiply, invert, find determinants, rank, and RREF.
Build and test transformation matrices for rotation, scaling, and translation.
Inspect small matrices or test linear systems before scaling up in code.
Check small stiffness matrices and system-of-equation setups for structural analysis.
Square matrices of size 2x2, 3x3, and 4x4. Eigenvalues are available for 2x2 and 3x3; larger systems are better handled in dedicated math software.
Yes. Any real number is accepted in the matrix cells, including negatives and decimals.
The inverse operation reports that the matrix is not invertible, and the determinant comes out as zero.
Every calculation runs locally in your browser. Your numbers and expressions are not transmitted or stored.