Matrix calculator
Calculator
The calculator needs JavaScript. The tables below give the same numbers for common cases.
How it is worked out
- Gaussian elimination with row swaps gives det = 1.
- 2 × 2 shortcut: ad − bc = 1.
| Inputs | Answer |
|---|---|
| Operation: Determinant of A; Matrix A: 2 1; 5 3; Matrix B: 1 0; 0 1 | The determinant of A is 1. |
| Operation: Inverse of A; Matrix A: 2 1; 5 3; Matrix B: 1 0; 0 1 | The inverse of A is 3 -1 | -5 2 (rows separated by |). |
| Operation: A × B; Matrix A: 1 2; 3 4; Matrix B: 5 6; 7 8 | A × B = 19 22 | 43 50. |
| Operation: Determinant of A; Matrix A: 1 2 3; 0 1 4; 5 6 0; Matrix B: 1 0; 0 1 | The determinant of A is 1. |
How to use it
Enter a matrix with spaces between numbers and semicolons between rows: 2 1; 5 3 is the matrix with rows (2, 1) and (5, 3). Choose the operation: determinant, inverse and transpose use matrix A; A + B and A × B use both.
The determinant and inverse need a square matrix; a matrix with determinant 0 has no inverse. For A × B the number of columns of A must equal the number of rows of B.
Frequently asked questions
What is the determinant of 2 1; 5 3?
2 × 3 − 1 × 5 = 1.
When does a matrix have an inverse?
When it is square and its determinant is not 0.
Can I multiply any two matrices?
Only when A has as many columns as B has rows.
Method: standard arithmetic shown step by step; no outside data is used. Checked 2026-11-12.
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