Matrix Calculator
inverse, determinant, augmented & diagonalize
Solve any matrix problem with the complete step-by-step method shown — addition, subtraction, multiplication, transpose, determinant, inverse, rank, augmented matrix systems and diagonalization. Built for TN Board, CBSE, JEE and NEET students — free and unlimited.
Enter your matrix (or matrices) to solve
1 2 newline 3 4.
Diagonalize supports matrices up to 3×3.
Free Online Matrix Calculator with Steps
This free matrix calculator solves matrix addition, subtraction, multiplication, transpose, determinant, rank/RREF, augmented matrix systems and diagonalization — with the complete step-by-step method shown every time, not just the final answer. It's built for Class 11–12, JEE and NEET students who need to verify their working or learn the correct method under exam conditions.
The inverse matrix calculator mode (also searched as "inverse of matrix calculator" and "inverse of a matrix calculator") uses Gauss-Jordan elimination on the augmented [A | I] matrix and shows the row operations used to reach the inverse, exactly as expected in board and JEE exams. The augmented matrix calculator mode solves a system of linear equations Ax = b by reducing [A | b] to reduced row-echelon form and reports whether the system has a unique solution, infinitely many solutions, or no solution. The diagonalize matrix calculator mode finds eigenvalues via the characteristic polynomial and the corresponding eigenvectors, for matrices up to 3×3.
If you're stuck on why a method works, or want the explanation in Tamil, StudyHelpAI's free AI Maths tutor breaks down matrix concepts step by step in English or Tamil.
← Back to Maths Homework HelpMatrix Calculator — Questions Answered
Yes — every mode (add, subtract, multiply, transpose, determinant, inverse, rank, augmented matrix and diagonalize) is completely free, with no sign-up, no daily limit and no ads. It runs entirely in your browser.
Switch to the "Inverse" tab, enter a square matrix in Matrix A, and click Solve. The calculator performs Gauss-Jordan elimination on [A | I] and shows the row operations, giving you A⁻¹ with the full working — this covers "inverse matrix calculator," "inverse of matrix calculator" and "inverse of a matrix calculator" searches, which all mean the same operation.
An augmented matrix combines a coefficient matrix A with a constants vector b as [A | b] to solve a system of linear equations Ax = b. The "Augmented" tab here reduces it to reduced row-echelon form and tells you whether the system has one solution, infinitely many, or none.
Diagonalizing a matrix A means finding a matrix P and a diagonal matrix D of eigenvalues such that A = PDP⁻¹. The "Diagonalize" tab finds the eigenvalues from the characteristic polynomial and one eigenvector per eigenvalue, for matrices up to 3×3.
Desmos has its own matrix tools inside its graphing calculator interface. This page is a standalone matrix calculator built specifically for step-by-step working — every result shows the row operations or elimination steps used, which Desmos' matrix tool does not display.
No — a "destiny matrix" is a numerology concept unrelated to mathematical matrices, and it's outside what StudyHelpAI covers. This page is a linear algebra matrix calculator for schoolwork and exam preparation (addition, inverse, determinant, diagonalization, and so on).
Yes. Every operation shows its method — row operations for the inverse and RREF, the elimination trace for the determinant, and the characteristic polynomial for diagonalization — so you can reproduce the same steps by hand.