Matrix Calculator
Add, subtract, multiply, transpose, find determinants and inverses of matrices up to 5×5 — instantly and accurately
Perform Matrix Operations
Result
How to Use the Matrix Calculator
Key Features
Addition & Subtraction
Perform element-wise addition or subtraction on matrices of matching dimensions with instant validation.
Matrix Multiplication
Multiply compatible matrices with automatic dimension checking. Columns of A must equal rows of B.
Transpose
Flip Matrix A over its diagonal — rows become columns and columns become rows in one click.
Determinant
Calculate determinants of square matrices up to 5×5 using recursive cofactor expansion method.
Matrix Inverse
Find the inverse of any non-singular square matrix using the adjugate-determinant method with validation.
Fully Responsive
Works seamlessly on phones, tablets, and desktops with scrollable grids and touch-friendly controls.
How Matrix Operations Work
C[i][j] = A[i][j] ± B[i][j]. Both matrices must share identical dimensions.C[i][j] = Σ(k=1 to p) A[i][k] × B[k][j]. Columns of A must equal rows of B.Aᵀ[i][j] = A[j][i]. Each row in the original becomes a column in the result.det = ad − bc. For larger square matrices, cofactor expansion is applied recursively: det(A) = Σ(j) (-1)^(1+j) × a₁ⱼ × det(M₁ⱼ).A⁻¹ = (1/det(A)) × adj(A), where adj(A) is the adjugate matrix — the transpose of the cofactor matrix. The inverse exists only when det(A) ≠ 0.Practical Examples
🇮🇳 Priya — Engineering Student, Chennai
Priya solves a system of 3 linear equations from her circuit analysis course. She sets up coefficient matrix A = [[2,1,−1],[−3,−1,2],[−2,1,2]] and constants B = [[8],[−11],[−3]].
She computes A⁻¹ and multiplies by B to find x=2, y=3, z=−1.
✓ Verification: 2(2)+1(3)+(−1)(−1) = 4+3+1 = 8 ✓
🇮🇳 Rohan — Data Scientist, Bengaluru
Rohan checks if a 3×3 covariance matrix is invertible before fitting a Gaussian model. Matrix = [[4,2,0],[2,5,1],[0,1,3]].
He calculates det(A) = 4(15−1) − 2(6−0) + 0 = 56 − 12 = 44.
✓ Determinant = 44 (non-zero) — matrix is invertible, model fitting proceeds.
🇺🇸 Sarah — Game Developer, San Francisco
Sarah multiplies a 2×3 transformation matrix by a 3×1 vertex vector. A = [[1,0,5],[0,1,3]], B = [[10],[20],[1]].
Result: [[1×10+0×20+5×1],[0×10+1×20+3×1]] = [[15],[23]].
✓ Screen position (15, 23) — translation applied correctly.
🇮🇳 Ananya — Economics Researcher, Delhi
Ananya transposes a 2×4 data matrix to switch observations and variables for input-output analysis. A = [[100,200,150,300],[50,75,80,120]].
✓ Aᵀ is 4×2 — Aᵀ[1][2] = A[2][1] = 50 — transpose verified correctly.
What Is a Matrix Calculator?
A matrix calculator is a computational tool designed to perform arithmetic and algebraic operations on matrices — rectangular arrays of numbers arranged in rows and columns. Matrices are the backbone of linear algebra, powering everything from search engine algorithms to structural engineering simulations.
This calculator supports six essential operations: addition, subtraction, multiplication, transposition, determinant computation, and matrix inversion. Each operation has strict dimensional requirements — for example, only square matrices have determinants, and multiplication requires the inner dimensions to match. The calculator validates these before computing.
Whether you're a student checking homework, an engineer verifying structural calculations, or a researcher exploring data transformations, this tool delivers instant and accurate results. Every calculation runs entirely in your browser — your matrix data never leaves your device.
Matrix Calculator in Multiple Languages
Want a deeper guide on matrix operations and real-world applications?
Read Our Complete Matrix Calculator Guide →Frequently Asked Questions
Is this matrix calculator free to use?
Yes, this matrix calculator is completely free with no signup required. All calculations run directly in your browser with no data sent to any server.
What matrix sizes does this calculator support?
This calculator supports matrices from 1×1 up to 5×5. You can set different dimensions for Matrix A and Matrix B independently.
Can I multiply matrices with different dimensions?
Yes, as long as the number of columns in Matrix A equals the number of rows in Matrix B. For example, a 2×3 matrix can be multiplied by a 3×4 matrix to produce a 2×4 result.
How is the determinant calculated?
The determinant is calculated using cofactor expansion (Laplace expansion) recursively. It only works for square matrices where rows equal columns.
What happens if the matrix has no inverse?
If the determinant of the matrix is zero (singular matrix), the calculator will display an error message explaining that the inverse does not exist.
Does this calculator work on mobile phones?
Yes, the matrix calculator is fully responsive and works on smartphones, tablets, and desktop computers.
Can I enter decimal or negative numbers?
Yes, you can enter integers, decimal numbers, and negative values in any matrix cell.
What is the difference between transpose and inverse?
Transpose flips a matrix over its diagonal — rows become columns. Inverse is the matrix that when multiplied by the original gives the identity matrix. Transpose always exists; inverse only exists for non-singular square matrices.
Are my calculations saved or stored anywhere?
No. All calculations happen entirely in your browser using JavaScript. No data is transmitted to any server.
How accurate are the results from this calculator?
Results use standard JavaScript floating-point arithmetic (64-bit double precision). Values are displayed rounded to 6 decimal places for clarity.
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