Matrix Calculator with Variables

Work with matrices containing letters, parameters, or mixed algebraic terms with confidence. Build expressions automatically while maintaining clear parentheses around every product and sum. Compute sums, differences, products, transposes, determinants, and adjugates for precision workflows. Find symbolic inverses using cofactors divided by the determinant for clarity. Export results as CSV or PDF with ease.

Matrix A
Matrix B
Example Data Table
MatrixEntries
A (2×2)[[a, b],[c, d]]
B (2×2)[[x, y],[z, t]]
det(A)(a)*(d) - (b)*(c)
A×B[[(a)*(x)+(b)*(z), (a)*(y)+(b)*(t)],[(c)*(x)+(d)*(z), (c)*(y)+(d)*(t)]]
A^{-1}(1/((a)*(d)-(b)*(c)))*[[d, -b],[-c, a]]
Result
Compute to see results here.
Formula Used
  • Add/Subtract: \((A \pm B)_{ij} = A_{ij} \pm B_{ij}\)
  • Multiply: \((A B)_{ij} = \sum_k A_{ik} B_{kj}\)
  • Transpose: \((A^\top)_{ij} = A_{ji}\)
  • Determinant: Laplace expansion along row 1 for \(n\ge 3\)
  • Adjugate: \(\mathrm{adj}(A) = \mathrm{cof}(A)^\top\)
  • Inverse: \(A^{-1} = \frac{1}{\det(A)} \mathrm{adj}(A)\) when \(\det(A)\neq 0\)
  • Trace: \(\mathrm{tr}(A) = \sum_i A_{ii}\)
How to Use This Calculator
  1. Pick matrix sizes for A and B as needed.
  2. Enter numbers, symbols, or expressions like 2a, x+y, or (p-q)/r.
  3. Select an operation: add, subtract, multiply, transpose, determinant, adjugate, inverse, trace, or scalar multiply.
  4. Click Compute to generate symbolic results with explicit parentheses.
  5. Use Download CSV or Download PDF to export the result.
FAQs

Yes. Entries accept numeric values, symbols, or composite expressions such as 3x, a+b, or (m-n)/p.

It preserves structure with parentheses but does not symbolically simplify; results show sums of products clearly and safely.

Determinants are computed up to 5×5 using expansion. Inverses are generated up to 4×4 via adjugate over determinant.

Blank inputs are treated as 0, ensuring well-defined expressions. You can explicitly enter 0 as well.

Yes. The CSV exporter writes a single cell when the result is scalar. The PDF exporter captures the result panel as a document.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.