Algebra

Matrix Operations Step by Step

By SC Editorial 2026-06-05 9 min read

Matrices organize numbers in rows and columns. They represent linear transformations, systems of equations, and computer graphics operations.

Matrix Addition

Add corresponding entries. Both matrices must have the same dimensions. Practice with our Matrix Calculator.

Matrix Multiplication

The product AB exists only when A's columns equal B's rows. Entry (i,j) is the dot product of row i of A and column j of B.

Determinants

For 2x2 matrix [[a,b],[c,d]], det = ad - bc. Determinants indicate whether a matrix is invertible. See the Determinant Calculator.

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