2×2 Matrix Multiplication

Math

2×2 Matrix Multiplication is a fast, free math calculator. Enter A[1,1], A[1,2] and A[2,1] to get an instant, accurate result — complete with the formula, a step-by-step worked example, and answers to common questions, all on one page and private to your browser.

Formula

C[i,j] = Σ_k A[i,k] × B[k,j]
  • For 2×2: C11=a11·b11+a12·b21, C12=a11·b12+a12·b22, etc.

[[1,2],[3,4]] × [[5,6],[7,8]]

Inputs
  • A[1,1]: 1
  • A[1,2]: 2
  • A[2,1]: 3
  • A[2,2]: 4
  • B[1,1]: 5
  • B[1,2]: 6
  • B[2,1]: 7
  • B[2,2]: 8

C = [[19,22],[43,50]]

Frequently asked questions

Is matrix multiplication commutative?
No: A×B ≠ B×A in general.