Matrix Calculator: Inverse, Determinant, Multiplication, Addition and Transpose
Type a matrix with one row per line and choose what to do. Answers are given as exact fractions where possible.
- Nothing you type is stored
- Free
- No signup
Inverse A⁻¹
3 × 3
- Determinant
- −1
Show working
- A = [2, 1, 1; 1, 3, 2; 1, 0, 0]
- det A = −1 ≠ 0
- [A | I] → row operations → [I | A⁻¹]
- A⁻¹ = [0, 0, 1; −2, 1, 3; 3, −1, −5]
- A·A⁻¹ = I ✓
Inverse A⁻¹
| C1 | C2 | C3 |
|---|---|---|
| 0 | 0 | 1 |
| −2 | 1 | 3 |
| 3 | −1 | −5 |
How to use
- Pick an operation: determinant, inverse, transpose, multiply, add or subtract.
- Type matrix A one row per line (and matrix B for multiply/add/subtract).
- Read the result matrix; open “Show working” for the method.
Good to know
Inverse: found by Gauss–Jordan elimination on [A | I]; for 2×2 it equals (1/det A)·[d, −b; −c, a]. A matrix has an inverse only if its determinant is not 0.
Multiplication: (AB)ᵢⱼ is row i of A times column j of B, so the columns of A must equal the rows of B. Order matters: AB is usually not BA.
Fractions are kept exact: the inverse of [4, 7; 2, 6] is shown as [3/5, −7/10; −1/5, 2/5], not rounded decimals. Separate numbers with spaces or commas; fractions like 1/2 are accepted.
Questions
How do I type a 3×3 matrix?
Three lines, three numbers on each, for example “2 1 1”, “1 3 2”, “1 0 0”.
Why does it say the matrix is singular?
Its determinant is 0, so it has no inverse. Its rows are not independent.
Why can’t I multiply these two matrices?
For A×B the number of columns in A must equal the number of rows in B. A 2×3 matrix can multiply a 3×n matrix.
Does it help with NCERT Class 12 matrices?
Yes, for checking inverses, products and determinants from the Matrices and Determinants chapters.
Is my data stored or sent anywhere?
No. The calculation runs entirely in your browser; nothing you type leaves your device.