Matrix calculator for operations, determinant and inverse
Paste matrices up to 5×5 and choose an operation. HitEquals validates dimensions and returns the result matrix, shape, determinant where defined and row norms.
Inputs used by this calculator
Matrix Calculator uses the fields below. The starting values reproduce the page example; replace them with values from the same units and time period before using the result.
| Input | Starting example | Accepted value | How it is used |
|---|---|---|---|
| Operation | A × B | A + B · A − B · A × B · 3 more choices | Supplies the operation quantity used by the published equation or result breakdown. |
| Matrix A — rows on new lines, values separated by spaces or commas | 1 2 3 4 | Text or a list in the format shown | Supplies the matrix a — rows on new lines, values separated by spaces or commas quantity used by the published equation or result breakdown. |
| Matrix B — used for +, − and × | 5 6 7 8 | Text or a list in the format shown | Supplies the matrix b — used for +, − and × quantity used by the published equation or result breakdown. |
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 are rounded for display in US format, with money in dollars and cents; CSV exports keep full calculation precision. This is a calculation summary, not an official certificate.