Matrix Calculator

Determinant, inverse, transpose and matrix multiplication

Quick Answer

Matrix Calculator: Determinant, inverse, transpose and matrix multiplication. 2×2 determinant = ad − bc · 3×3: Sarrus' rule.

Matrix A (2×2)

Matrix B (2×2)

Result

1922

4350

Determinant meaning

det(A)	Meaning
det ≠ 0	Invertible; Ax=b has unique solution
det = 0	Singular; no inverse; rows dependent
\|det\| (2×2)	Area scale factor of the linear map
\|det\| (3×3)	Volume scale factor
det < 0	Orientation flipped (mirror)

💡 Input format: one row per line, values separated by commas or spaces. Matrix multiplication is NOT commutative — A×B ≠ B×A in general.

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Key capability: Determinant, inverse, transpose and matrix multiplication.
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Matrix operations

2×2 determinant = ad − bc · 3×3: Sarrus' rule

Inverse A⁻¹ = adj(A) ÷ |A| (exists iff |A| ≠ 0)

Multiply: (AB)[i][j] = Σₖ A[i][k]×B[k][j]

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Open the page and fill in the input fields — results update automatically. Determinant, inverse, transpose and matrix multiplication.

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Standard mathematical formulas. All logic verified. Last updated: 2025-07

Last updated: 2026-08-04

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Results provided by this tool are for reference only and do not constitute professional advice.