Matrix Calculator
Add, multiply, transpose, and find determinant/inverse of matrices
About Matrix Operations
Matrices are rectangular arrays of numbers used in linear algebra, physics, computer graphics, and machine learning.
- Addition/Subtraction: Add/subtract corresponding elements (same-size matrices only).
- Multiplication: Row-by-column dot products. A(m×n) × B(n×p) = C(m×p).
- Transpose: Swap rows and columns. Element (i,j) becomes (j,i).
- Determinant: Scalar value from square matrix. det=0 means singular (not invertible).
Frequently Asked Questions
How do you multiply matrices?
Multiply each row element of matrix A by the corresponding column element of matrix B, sum the products for each result cell.
What is a determinant?
A scalar computed from a square matrix. For 2x2 [a,b;c,d]: det = ad - bc. Tells if matrix is invertible.
When is a matrix invertible?
When its determinant is not zero. The inverse A^(-1) satisfies A × A^(-1) = Identity matrix.