Matrix Calculator
Perform matrix operations including addition, subtraction, multiplication, determinant, inverse, and more with our comprehensive matrix calculator.
Matrix Operations
Result
Calculation History
Understanding Matrices
What is a Matrix?
A matrix is a rectangular array of numbers arranged in rows and columns. Matrices are fundamental in linear algebra and have applications in computer graphics, physics, and engineering.
Matrix Dimensions
A matrix with m rows and n columns is called an m×n matrix. The dimensions are always written as rows × columns.
Special Types of Matrices
- Square Matrix: Same number of rows and columns
- Identity Matrix: Square matrix with 1s on diagonal and 0s elsewhere
- Zero Matrix: All elements are zero
- Diagonal Matrix: Non-zero elements only on the main diagonal
Matrix Questions & Answers
How do you add or subtract matrices?
Matrices must have the same dimensions to be added or subtracted. You simply add or subtract corresponding elements:
A + B = [a₁₁+b₁₁, a₁₂+b₁₂]
[a₂₁+b₂₁, a₂₂+b₂₂]
How does matrix multiplication work?
Matrix multiplication requires the number of columns in the first matrix to equal the number of rows in the second matrix. The product AB has dimensions (rows of A) × (columns of B). Each element is the dot product of a row from A and a column from B.
What is a matrix determinant?
The determinant is a scalar value that can be computed from a square matrix. For a 2×2 matrix:
det([a b; c d]) = ad - bc
Determinants are used to solve systems of linear equations, find inverses, and in transformations.
What does it mean for a matrix to be invertible?
A square matrix is invertible (non-singular) if there exists a matrix B such that AB = BA = I (identity matrix). A matrix is invertible if and only if its determinant is not zero. The inverse is useful for solving matrix equations.
Matrix Calculator Answers
What does the matrix calculator do?
The matrix calculator performs various operations on matrices, such as addition, subtraction, multiplication, finding the determinant, inverse, transpose, and more.
What types of matrices can it handle?
It works with square and rectangular matrices of different dimensions. Some features (like determinants or inverses) require square matrices.
Can it solve systems of equations?
Yes. The calculator can solve linear systems using matrix methods like Gaussian elimination or by finding the inverse matrix (if applicable).
Does it show step-by-step solutions?
Many matrix calculators provide detailed steps, especially for operations like row reduction, determinant computation, and inverse calculation—helpful for learning or verification.