Matrix Multiply Calculator
Multiply two 2×2 matrices and get the resulting matrix and its determinant.
Last updated · View algorithm, constants and default inputs (JSON)
About this calculator
Matrix multiplication combines rows of the first matrix with columns of the second. Unlike ordinary multiplication it is not commutative, so the order of the matrices matters.
Worked example
calculated with the default values below
A row 1 col 1 1 · A row 1 col 2 2 · A row 2 col 1 3 · A row 2 col 2 4 · B row 1 col 1 5 · B row 1 col 2 6 · B row 2 col 1 7 · B row 2 col 2 8 Result r1c1 19.0000 · Result r1c2 22.0000 · Result r2c1 43.0000 · Result r2c2 50.0000 · Determinant of A -2.0000 · Determinant of B -2.0000 · Determinant of product A × B 4.0000
General background references
Disclaimer
These calculators give general mathematical results. They suit study, planning and estimation — verify anything that feeds a graded submission, a published figure or a financial commitment.
Implementation source
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
Formula and variables
C = A × B; det(C) = c11 × c22 − c12 × c21; det(A) = a11 × a22 − a12 × a21
- cᵢⱼ
- element of product C
- aᵢₖ
- element of A
- bₖⱼ
- element of B
- C
- C = A × B (2×2)
- det(AB)
- determinant of the product matrix
Standard 2×2 matrix product; k runs 1–2. Determinants of A and B are ad − bc for each input matrix.
Frequently asked questions
What is the determinant of the product matrix?
The calculator multiplies A × B and computes det(C) from the four result entries. For 2×2 matrices, det(A × B) also equals det(A) × det(B), which can be used as a consistency check.