Matrix Calculator
Adjust the inputs below. Results update as you type.
How it works
Matrix multiplication: (AB)ᵢⱼ = Σ Aᵢₖ Bₖⱼ—not commutative (AB ≠ BA generally). Determinant of 2×2: ad − bc. Inverse exists only when det ≠ 0. Gauss-Jordan elimination finds the inverse by row-reducing [A|I] to [I|A⁻¹]. Matrices model linear transformations, solve systems of equations, and represent adjacency in graph theory.
Input guidance
- Check units and decimal placement before running calculations.
- For percentage and ratio tasks, define the baseline value clearly.
- Use rounded output carefully and keep full precision for intermediate steps.
The formula
Matrices add element-wise and multiply by the row-by-column rule: each entry is the dot product of a row and a column. The determinant and inverse apply to square matrices.
Worked example
Multiplying a 2×3 matrix by a 3×2 matrix gives a 2×2 result; the inner dimensions (3) must match.
More examples to test
- Baseline example: solve with clean numbers first to verify formula direction.
- Edge-case example: test near-zero or boundary values to avoid interpretation errors.
How to interpret results
Use outputs as quick checks, then verify with step-by-step work for graded or high-stakes use.
When this can be inaccurate
Errors usually come from unit mismatch, wrong baseline assumptions, or rounding too early in multistep problems.
Change history
- July 2026: Quality-reviewed for publication with formula checks and explanatory copy updates.
Site-wide corrections also appear on the corrections log.
Build math and logic skills with guided lessons
Educational platform recommendation.
Frequently asked questions
When can two matrices be multiplied?+
When the number of columns in the first equals the number of rows in the second. The result takes the outer dimensions.
What is a determinant?+
A single number computed from a square matrix that indicates whether it is invertible and how it scales area or volume.
Is matrix multiplication commutative?+
No. In general AB ≠ BA, so the order of multiplication matters for matrices.
Why do my classroom and calculator results differ?+
Differences usually come from rounding conventions, order-of-operations handling, or different baseline assumptions.
What is the safest way to validate an answer?+
Recompute with units shown and check against a second method or manual arithmetic for critical problems.