Math Tool✨ New Release
Matrix Calculator
Perform matrix arithmetic operations including matrix addition, subtraction, multiplication, and transpose for 2x2 and 3x3 matrices with step-by-step matrix calculations.
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Interactive Matrix Calculator Workspace
Matrix A
Matrix B
Result Output Matrix
68
1012
Step-by-Step Matrix Operations
Cell [Row 1, Col 1]: A[0][0] + B[0][0] = 1 + 5 = 6
Cell [Row 1, Col 2]: A[0][1] + B[0][1] = 2 + 6 = 8
Cell [Row 2, Col 1]: A[1][0] + B[1][0] = 3 + 7 = 10
Cell [Row 2, Col 2]: A[1][1] + B[1][1] = 4 + 8 = 12
Mathematical Formula & Variables
Equation Model
C[i][j] = A[i][j] ± B[i][j] | C[i][j] = ∑ (A[i][k] × B[k][j])For addition and subtraction, elements are added or subtracted individually. For matrix multiplication, rows of the first matrix are multiplied element-wise by columns of the second matrix.
Variable Definitions
| Symbol | Description |
|---|---|
| A | The first input matrix of dimensions m × n |
| B | The second input matrix of dimensions n × p |
| C | The resulting output matrix |
How to Use the Matrix Calculator
- Choose the matrix dimensions (2x2 or 3x3) and your preferred operation (Addition, Subtraction, Multiplication, or Transpose).
- Fill in the numeric inputs for Matrix A (and Matrix B, if applicable).
- Click calculate to view the complete step-by-step intermediate calculations and the final result matrix.
Practical Example Calculation
Scenario Context: Multiplying two 2x2 matrices: A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]].
Step 1: Calculate row 1, col 1: (1×5) + (2×7) = 5 + 14 = 19.
Step 2: Calculate row 1, col 2: (1×6) + (2×8) = 6 + 16 = 22.
Step 3: Calculate row 2, col 1: (3×5) + (4×7) = 15 + 28 = 43.
Step 4: Calculate row 2, col 2: (3×6) + (4×8) = 18 + 32 = 50.
The product matrix is [[19, 22], [43, 50]].
Frequently Asked Questions
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