Matrix Algebra Answers

Quick answers to common linear algebra questions with formulas, worked examples, and step-by-step explanations.

All Answers

How Do I Find the Inverse of a 2x2 Matrix?

For [[a,b],[c,d]], the inverse is (1/(ad-bc)) * [[d,-b],[-c,a]]. Worked example with step-by-step formula for quick calculation.

How Do I Calculate a 3x3 Determinant?

Cofactor expansion along the first row: det = a(ei-fh) - b(di-fg) + c(dh-eg). Step-by-step formula and worked example.

What Are the Rules for Matrix Multiplication?

A(m*n) * B(n*p) = C(m*p). Inner dimensions must match. Element C[i][j] = sum of A[i][k] * B[k][j] for all k.

Try the Interactive Calculator

All of these operations are available in the ML3X Matrix Calculator, which supports matrices up to 5×5 with full step-by-step solution display.

Built by Michael Lip. Try the ML3X Matrix Calculator for interactive step-by-step solutions.

Interactive Linear Algebra Cheatsheet — Formulas with Mini-Calculators

Searchable linear algebra formula reference with interactive Try It calculators. Covers determinants, inverses, rank, trace, eigenvalues, norms, and decompositions. Filterable by category.

Matrix Operations Reference — Interactive Cheatsheet with Visual Examples

Interactive matrix operations cheatsheet covering 20+ operations: addition, multiplication, transpose, inverse, determinant, eigenvalues, decompositions. Each entry has formula, visual example, and a try-it mini-calcu...