2x2 Matrix Addition & Subtraction Calculator
Add or subtract 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+B
- [[6, 8], [10, 12]]
- A-B
- [[-4, -4], [-4, -4]]
Quick answer
Matrices are added or subtracted entry by entry, so the result has the same shape as the inputs.
(A±B)[i][j] = A[i][j] ± B[i][j]
At a glance
| What it does | Add or subtract two 2x2 matrices. |
|---|---|
| Category | Math |
| Inputs needed | A11, A12, A21, A22, B11, B12, B21, B22 |
| Main output | A+B |
| Formula | (A±B)[i][j] = A[i][j] ± B[i][j] |
| Cost | Free — no sign-up, no download |
How to use the 2x2 Matrix Addition & Subtraction Calculator
- 1Enter all four entries for matrix A and matrix B.
- 2The calculator adds and subtracts entry by entry.
- 3Both results have the same 2x2 shape as the inputs.
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
- A213
- A224
- B115
- B126
- B217
- B228
Results
- A+B[[6, 8], [10, 12]]
- A-B[[-4, -4], [-4, -4]]
Frequently asked questions
Can I add matrices of different sizes?
No — addition and subtraction require matrices of the exact same dimensions.
Does order matter for subtraction?
Yes, A-B is the negative of B-A.
What do I need to enter into the 2x2 Matrix Addition & Subtraction 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 Addition & Subtraction Calculator work out the answer?
Matrices are added or subtracted entry by entry, so the result has the same shape as the inputs. It applies the formula (A±B)[i][j] = A[i][j] ± B[i][j] and shows the working so you can check each step by hand.
Is the 2x2 Matrix Addition & Subtraction 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.