Matrix Calculators: Operations, Inverses and Eigenvalues

Use these matrix calculators to work through linear algebra problems without doing every step by hand. Addition of Two Matrices, Subtraction of Two Matrices, and Matrix Multiplication handle common operations, while Inverse Matrix 3×3 and Rank of 3×3 Matrix help you examine a matrix’s properties. You can also calculate eigenvalues and eigenvectors for 2×2 or 3×3 matrices, square a matrix, and work with determinants. These tools are useful for students checking coursework, educators preparing examples, and engineers or scientists working with matrix-based models.

Eigenvalues and Eigenvectors 3×3

Enter the nine entries of a 3×3 matrix to find its eigenvalues and eigenvectors, plus the determinant, trace and characteristic polynomial. Includes a worked example you can reproduce with the default values.

Inverse Matrix 3×3

Enter the nine entries of a 3×3 matrix to find its inverse, determinant, and adjugate. The calculator uses the adjugate (cofactor) method and tells you when the matrix is singular.

Matrix Squared

This calculator computes the square of a 2×2 or 3×3 matrix, i.e. the product A × A. Enter the matrix elements and get the resulting squared matrix instantly.

Matrix Multiplication

Multiply two matrices of compatible sizes (up to 3 × 3) instantly. Choose the dimensions of matrix A and B, enter their elements, and get the full product matrix A × B.

Determinant Multiplication

Enter two square matrices (2×2 or 3×3) and instantly get det(A), det(B), and their product. Based on the multiplicative property of determinants: det(AB) = det(A)·det(B).

Eigenvalues and Eigenvectors 2×2

Enter the four elements of a 2×2 matrix to get its eigenvalues and eigenvectors, plus the determinant, trace, and characteristic polynomial with a full worked solution.

Rank of 3×3 Matrix

Enter the nine entries of a 3×3 matrix to find its rank instantly. The calculator uses Gaussian elimination and works for any matrix, including singular ones where the determinant is zero.

Matrix Trace

Enter the entries of a 2 × 2 or 3 × 3 square matrix and instantly get its trace — the sum of the main diagonal elements a₁₁ + a₂₂ (+ a₃₃).

Determinant

Compute the exact determinant of any square matrix from 2×2 to 6×6. Enter your entries as integers, decimals or fractions and get the exact result, a decimal value, singularity check and step-by-step solution.

Sum of Determinants

Enter the entries of two square matrices (2 × 2 or 3 × 3) and this calculator finds each determinant and their sum |A| + |B| instantly, with step-by-step formulas explained.

Addition of Two Matrices

Add two matrices of the same size (2×2 or 3×3) by entering their elements. The calculator sums corresponding entries and displays the resulting matrix instantly.

Matrix Transpose

Enter the entries of a 2 × 2 or 3 × 3 matrix and this calculator instantly swaps its rows and columns to produce the transposed matrix Aᵀ, shown as a table.

Matrix Scalar Multiplication

Multiply a 2 × 2 or 3 × 3 matrix by a scalar (constant). Enter the scalar k and the entries of matrix A to get the resulting matrix kA instantly.

Subtraction of Two Matrices

Subtract a 2×2 or 3×3 matrix B from matrix A element by element. Enter the values of both matrices and get the resulting matrix C = A − B instantly, with the formula and a worked example.