Complete guide
Matrix calculator for operations, determinant and inverse
Paste matrices up to 5×5 and choose an operation. Calculator24 validates dimensions and returns the result matrix, shape, determinant where defined and row norms.
Entering a matrix
Put each row on a new line and separate values with spaces or commas. Every row in one matrix must have the same number of columns.
Addition and subtraction
Matrices must share the same shape; combine corresponding entries.
Matrix multiplication
The columns of A must equal the rows of B. Output shape is rows of A by columns of B.
(AB)ᵢⱼ=ΣₖaᵢₖbₖⱼDeterminant and invertibility
A determinant is defined for square matrices. A zero determinant means the matrix has no inverse.
Gauss–Jordan inverse
Augment A with the identity matrix and use row operations until the left side becomes identity; the right side is A⁻¹.
Numerical limitations
Floating-point elimination can magnify error for nearly singular matrices. Scientific computing may require condition-number analysis and specialized linear algebra libraries.
Matrix dimension rules
| Operation | Requirement | Output shape |
|---|---|---|
| A±B | same shape | same shape |
| AB | c(A)=r(B) | r(A)×c(B) |
| det(A) | A square | scalar |
| A⁻¹ | A square, det≠0 | same shape |
Frequently asked questions
How do I separate rows?
Use a new line for each row.
Can I use commas?
Yes, spaces and commas separate entries.
Why can matrix multiplication fail?
The first matrix column count must equal the second matrix row count.
When is a matrix invertible?
A square matrix is invertible when its determinant is nonzero.
How large can matrices be?
Up to 5×5.
Are decimal answers exact?
They are floating-point approximations.
What to keep in mind
Matrices may contain up to 5 rows and 5 columns with finite numeric entries. Inversion requires a square nonsingular matrix. Decimal results are numerical approximations.
Results display up to 8 decimal places; exported numbers preserve calculation precision. This is a calculation summary, not an official certificate.