Matrix Calculator
Perform matrix operations with step-by-step solutions
Matrix Calculator
Use our matrix calculator below to perform operations like addition, subtraction, multiplication, determinant, inverse, and transpose on matrices.
š Calculation Results
Select a matrix operation to see results here
š Understanding Matrix Operations
Matrix Addition
Matrix addition can only be performed on matrices of the same size. Add corresponding elements in the same positions.
Matrix Multiplication
For matrix multiplication AĆB, the number of columns in A must equal the number of rows in B. The result is computed using dot products.
Determinant
The determinant is a scalar value computed from square matrices. It's used in linear algebra and for computing matrix inverses.
What is a Matrix?
A matrix, in a mathematical context, is a rectangular array of numbers, symbols, or expressions that are arranged in rows and columns. Matrices are often used in scientific fields such as physics, computer graphics, probability theory, statistics, calculus, numerical analysis, and more.
The dimensions of a matrix, A, are typically denoted as m Ć n. This means that A has m rows and n columns. When referring to a specific value in a matrix, called an element, a variable with two subscripts is often used to denote each element based on its position in the matrix.
Common Matrix Operations
- Addition: Add corresponding elements of matrices with the same dimensions
- Subtraction: Subtract corresponding elements of matrices with the same dimensions
- Multiplication: Use dot product to multiply matrices (requires compatible dimensions)
- Transpose: Flip matrix over its diagonal, switching rows and columns
- Determinant: Calculate a scalar value from a square matrix
- Inverse: Find the matrix that, when multiplied with the original, gives the identity matrix