Result
Enter values and select Calculate.
Formula and methodology
Addition and subtraction require identical dimensions; multiplication requires columns(A) = rows(B). Determinant, inverse, and RREF use elimination with partial pivoting. A relative pivot tolerance of 10⁻¹² identifies numerically negligible pivots.
Worked example
For A = [[1, 2], [3, 4]], det(A) = −2, A⁻¹ = [[−2, 1], [1.5, −0.5]], and A × A = [[7, 10], [15, 22]].
Assumptions and boundaries
- Matrix dimensions are limited to 1×1 through 6×6.
- A singular or numerically near-singular matrix does not have a reliable inverse here.
- RREF and inverse results use floating-point arithmetic with controlled display rounding.
- System of Equations Calculator remains the tool for solving equation systems.
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