2x2 Matrix Multiplication Calculator
Multiply two 2x2 matrices.
Enter your values
Enter the a11 you are working with.
Enter the a12 you are working with.
Enter the a21 you are working with.
Enter the a22 you are working with.
Enter the b11 you are working with.
Enter the b12 you are working with.
Enter the b21 you are working with.
Enter the b22 you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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]
At a glance
| What it does | Multiply two 2x2 matrices. |
|---|---|
| Category | Math |
| Inputs needed | A11, A12, A21, A22, B11, B12, B21, B22 |
| Main output | A x B |
| Formula | (AB)[i][j] = sum_k A[i][k]*B[k][j] |
| Cost | Free — no sign-up, no download |
How to use the 2x2 Matrix Multiplication Calculator
- 1Enter the entries of matrix A and matrix B in row-major order.
- 2The calculator multiplies rows of A by columns of B.
- 3Read the resulting 2x2 product matrix.
Inputs explained
- A11
- Enter the a11 you are working with.
- A12
- Enter the a12 you are working with.
- A21
- Enter the a21 you are working with.
- A22
- Enter the a22 you are working with.
- B11
- Enter the b11 you are working with.
- B12
- Enter the b12 you are working with.
- B21
- Enter the b21 you are working with.
- B22
- Enter the b22 you are working with.
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.
What do I need to enter into the 2x2 Matrix Multiplication Calculator?
Just 8 values: a11, a12, a21, a22, b11, b12, b21, b22. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the 2x2 Matrix Multiplication Calculator work out the answer?
Each entry of the product is the dot product of a row of A with a column of B. It applies the formula (AB)[i][j] = sum_k A[i][k]*B[k][j] and shows the working so you can check each step by hand.
Is the 2x2 Matrix Multiplication Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.