Matrix Addition and Subtraction Calculator
Add or subtract matrices of the same dimensions.
Calculate Matrix Addition/Subtraction
Matrix Addition/Subtraction Examples
2×2 Addition
A: 1,2;3,4
B: 5,6;7,8
Result: 6,8;10,12
2×2 Subtraction
A: 5,6;7,8
B: 1,2;3,4
Result: 4,4;4,4
Zero Matrix
A: 1,2;3,4
B: 0,0;0,0
Result: 1,2;3,4 (same as A)
How to Calculate Matrix Addition/Subtraction
Requirements
Matrices must have the same dimensions (same number of rows and columns).
Addition
Add corresponding elements: (A + B)[i,j] = A[i,j] + B[i,j]
Subtraction
Subtract corresponding elements: (A - B)[i,j] = A[i,j] - B[i,j]
Properties
- Commutative: A + B = B + A
- Associative: (A + B) + C = A + (B + C)
- Identity: A + 0 = A (where 0 is zero matrix)
- Inverse: A + (-A) = 0
Special Cases
- Zero matrix: A + 0 = A
- Negative matrix: A - A = 0
- Scalar addition: A + kI (where I is identity)