⊞ Matrix Calculator (2×2 and 3×3)

Matrix A

Matrix B

Result

Matrix Operations Guide

A matrix is a rectangular array of numbers arranged in rows and columns. Matrix operations are fundamental in linear algebra, computer graphics, engineering, and machine learning.

Basic Matrix Operations

  • Addition/Subtraction: Add or subtract corresponding elements. Matrices must be same size.
  • Multiplication: For A(m×n) × B(n×p), the inner dimensions must match. Result is m×p.
  • Transpose (Aᵀ): Flip rows and columns — rows become columns.
  • Determinant: A scalar value that describes certain properties of the matrix.
det([[a,b],[c,d]]) = ad − bc

Frequently Asked Questions

When can you multiply two matrices? ▼
Matrix multiplication A×B is only possible when the number of columns in A equals the number of rows in B. A(m×n) × B(n×p) = C(m×p).
What is a matrix determinant used for? ▼
The determinant tells you if a matrix is invertible (non-zero = invertible), and is used in solving systems of linear equations, finding eigenvalues, and computing cross products.
What does matrix transpose mean? ▼
Transposing a matrix flips it over its main diagonal — rows become columns and columns become rows. If A is 2×3, Aᵀ is 3×2.