Matrix Math Made Simple: Add, Multiply, Determinant

Published Apr 13, 2026 · 6 min read

Matrices are rectangular arrays of numbers used everywhere from computer graphics to machine learning. Here are the essential operations.

Matrix Addition

Add corresponding elements. Matrices must be the same size.

Matrix Multiplication

Not element-by-element! To multiply A(m×n) by B(n×p), each element in the result is the dot product of a row from A and a column from B. The result is m×p. Order matters: AB ≠ BA.

Determinant (2×2)

det(A) = ad − bc for matrix [[a,b],[c,d]]

If the determinant is zero, the matrix has no inverse (it's singular).

Why This Matters

Solving linear equations — Ax = b can be solved with A⁻¹b
Computer graphics — Rotation, scaling, and transformation are matrix operations
Data science — Covariance matrices, PCA, neural network weights

Try it: Use our Matrix Calculator to perform addition, multiplication, determinant, and inverse operations.

📚 Sources: Khan Academy EPA