Matrix Calculator
Perform matrix operations: addition, subtraction, multiplication, transpose, and determinant for 2×2 and 3×3 matrices.
Inputs
Matrix A (2×2)
Matrix B (2×2)
Results
Matrix Operations
Matrices are rectangular arrays of numbers. Matrix multiplication (A×B) requires A's columns = B's rows. The determinant of a 2×2 matrix [a,b;c,d] = ad−bc. If det≠0, the matrix is invertible. Matrices are used in linear algebra, computer graphics, physics, and machine learning.
What is the Matrix Calculator?
The Matrix Calculator is a collegiate-level Linear Algebra tool used to perform complex operations on multi-dimensional data grids. It easily handles matrix addition, subtraction, multiplication, determinants, and inverses.
How It Works (Algorithm)
Matrices follow very strict arithmetic rules. While addition simply adds corresponding cells ($a_{11} + b_{11}$), matrix multiplication uses complex row-by-column "dot products". The calculator automates these tedious, error-prone linear algebra computations instantly.
$$ c_{ij} = \sum_{k=1}^{n} a_{ik} b_{kj} $$
The summation dot-product rule for Matrix Multiplication.
How to Use It
Set the physical dimensions (Rows and Columns) for Matrix A and Matrix B. Fill in the data cells for both grids. Select your desired operation from the dropdown, and the tool will instantly compute the resulting matrix.