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Matrix Calculator
Perform basic operations on matrices, including addition, subtraction, multiplication, determinant, transpose, and inverse. Supports dimensions up to 4x4 with step-by-step calculations.
Matrix Calculations
Result
Step-by-step
How to calculate matrix operations
Matrices are rectangular arrays of numbers. Basic calculations include:
- Matrix Addition/Subtraction: Add or subtract corresponding elements. Both matrices must have identical dimensions.
- Matrix Multiplication (A × B): The number of columns in Matrix A must equal the number of rows in Matrix B. Multiply rows of A by columns of B, summing the products.
- Determinant: A scalar value calculated for square matrices, reflecting scaling factor and invertibility.
- Transpose: Swap rows and columns, turning an m × n matrix into an n × m matrix.
- Inverse: Find a matrix that, multiplied by the original, yields the identity matrix. Only square matrices with non-zero determinants have inverses.
FAQ
Can you multiply any two matrices?
No. You can only multiply Matrix A and Matrix B (A × B) if the number of columns in Matrix A is exactly equal to the number of rows in Matrix B.
What is the transpose of a matrix?
The transpose of a matrix is formed by swapping its rows and columns. For any element aij, it moves to position aji.
What is an identity matrix?
An identity matrix is a square matrix with ones along the main diagonal (top-left to bottom-right) and zeros everywhere else.