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2x2 Matrix Multiplication Calculator

Multiply two 2x2 matrices.

Enter your values

ⓘ Live results

Results
A x B
[[4, 6], [1, 3]]
Top-left entry
4
Bottom-right entry
3

Quick answer

Each entry of the product is the dot product of a row of A with a column of B.

(AB)[i][j] = sum_k A[i][k]*B[k][j]

How to use the 2x2 Matrix Multiplication Calculator

  1. 1Enter the entries of matrix A and matrix B in row-major order.
  2. 2The calculator multiplies rows of A by columns of B.
  3. 3Read the resulting 2x2 product matrix.

Worked example

Using the values the calculator loads with:

Inputs

  • A111
  • A122
  • A210
  • A221
  • B112
  • B120
  • B211
  • B223

Results

  • A x B[[4, 6], [1, 3]]
  • Top-left entry4
  • Bottom-right entry3

Frequently asked questions

Is matrix multiplication commutative?

No — AB usually does not equal BA.

Can I multiply matrices of other sizes?

This tool is built for 2x2; the same row-times-column rule extends to other compatible sizes.

About this calculator

Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.