Matrix Calculator

What this calculator does

The Matrix Calculator performs common operations on matrices: addition, subtraction, multiplication, determinant, inverse, transpose, and squaring. It accepts matrices up to six rows and six columns and reports the result in a compact grid.

Matrices are rectangular arrays of numbers used to represent systems of equations, transformations, graph networks, and data sets. Matrix operations are central to linear algebra, computer graphics, machine learning, and engineering.

How to use this calculator

1. Enter matrix A. Put one row per line and separate values with spaces or commas.
2. For addition, subtraction, or multiplication, enter matrix B in the same format.
3. Choose an operation.
4. Click Calculate.

For example, matrix A can be entered as:

1 2
3 4

The default example multiplies A by B and returns a 2 × 2 result.

Matrix operations

A + B       element-wise addition
A − B       element-wise subtraction
A × B       matrix multiplication
det(A)      determinant of a square matrix
A⁻¹         inverse of a square matrix
Aᵀ          transpose of A
A²          A multiplied by itself

Addition and subtraction require matrices with the same dimensions. Multiplication requires the number of columns in A to equal the number of rows in B. Determinants, inverses, and squares require square matrices.

What the results mean

The result panel shows the dimensions of the result and the matrix or scalar value. For multiplication, each entry in the result is the dot product of a row from A and a column from B. For a determinant, the result is a single number that describes how the matrix scales area or volume. A determinant of zero means the matrix is singular and has no inverse.

The transpose swaps rows and columns. The inverse of a matrix A is the matrix that produces the identity matrix when multiplied by A.

Assumptions and limitations

• Each matrix may have up to six rows and six columns.
• Every row must contain the same number of values.
• Entries must be finite numbers. Fractions are not accepted directly; convert them to decimals first.
• The inverse is computed with Gauss-Jordan elimination and partial pivoting. A singular matrix is rejected.
• Results are displayed to at most six decimal places.
• The calculator does not support symbolic matrices, complex entries, or eigenvalues.

Frequently asked questions

Why does matrix multiplication require matching dimensions?

Each result entry is a dot product of a row from A and a column from B. The row and column must have the same number of entries, so the number of columns in A must equal the number of rows in B.

What does a zero determinant mean?

A zero determinant means the matrix is singular. It does not have an inverse, and the linear transformation it represents collapses at least one dimension. The calculator reports an error when you ask for the inverse of a singular matrix.

Can I add a 2 × 3 matrix to a 3 × 2 matrix?

No. Addition and subtraction require exactly the same dimensions. A 2 × 3 matrix and a 3 × 2 matrix can be multiplied, but their sum is undefined.

How do I enter a matrix with fractions?

Convert each fraction to a decimal before entering it. For example, enter 0.5 instead of 1/2. The result is then displayed as a decimal.

Source

Reference: Calculator.net — Matrix Calculator.