Matrix Calculator

The Matrix Calculator performs the core operations of linear algebra on 2×2 and 3×3 matrices: addition, subtraction, multiplication, transpose, determinant, and inverse. Every result is computed with exact rational arithmetic, so answers that are fractions stay fractions — 1/3 never silently becomes 0.333333 unless you ask for it.

How to use it

1. Pick a matrix size — 2 × 2 or 3 × 3. The grid of cells resizes to match.
2. Choose an operation. Binary operations (add, subtract, multiply) reveal a second matrix, B; transpose, determinant, and inverse work on matrix A alone, so B is hidden for them.
3. Fill in the cells. You can type whole numbers, decimals like 0.5, or exact fractions like 1/2 or -2/5. Empty cells are treated as 0.
4. Select the output format — Fraction (exact) keeps every value as a reduced fraction, while Decimal rounds to six places.

The result appears as a grid. For the determinant and inverse, a step-by-step working panel shows exactly how the answer was reached.

What each operation does

• Add / Subtract combine two same-size matrices element by element.
• Multiply is true matrix multiplication — each result cell is the dot product of a row of A with a column of B, not an element-wise product.
• Transpose flips A across its main diagonal, turning rows into columns.
• Determinant uses ad − bc for a 2×2 matrix and full cofactor expansion for a 3×3.
• Inverse is computed from the adjugate (the transpose of the cofactor matrix) divided by the determinant.

Why exact fractions matter

Inverting an integer matrix almost always produces fractions. The inverse of [[2, 1], [0, 3]], for example, is [[1/2, -1/6], [0, 1/3]]. Because the calculator keeps a numerator and denominator as integers and reduces them with the greatest common divisor, these values are printed exactly rather than as lossy decimals. Switch to decimal mode only when you want a rounded, at-a-glance figure.

What happens with a singular matrix?

A matrix whose determinant is 0 has no inverse. Rather than dividing by zero, the calculator detects this and returns a clear message explaining that the matrix is singular.

Is my data sent anywhere?

No. All calculations run entirely in your browser — the matrices you enter never leave your device.

Which sizes are supported?

Square matrices of size 2 × 2 and 3 × 3. These cover the overwhelming majority of hand-worked linear-algebra problems, homework, and quick checks.