What matrix sizes does this calculator support?

It works with numeric 1x1, 2x2, and 3x3 matrices only. Larger matrices, symbolic entries, and row-reduction workflows are outside its scope.

When can I add or subtract matrices?

Addition and subtraction require the same number of rows and columns in both matrices. If the shapes do not match, the operation is not defined.

When is matrix multiplication defined?

You can multiply A by B only when the number of columns in A equals the number of rows in B.

Why does inverse mode say the matrix is singular?

A matrix has an inverse only when its determinant is not zero. If det(A) = 0, the matrix is singular and inverse mode stops there instead of showing misleading output.

Does this calculator do symbolic algebra or solve full systems?

No. It is a small-matrix numeric workspace for checking arithmetic, not a symbolic algebra engine or a general linear-system solver.

Matrix Calculator

Check small-matrix arithmetic fast: add, subtract, multiply, transpose, find determinants, and invert 1x1 to 3x3 numeric matrices.

How It Works

Formula

A + B = [a_{ij} + b_{ij}]

AB = \left[\sum_{k=1}^{n} a_{ik} b_{kj}\right]

\det\begin{bmatrix} a & b \\ c & d \end{bmatrix} = ad - bc

A^{-1} = \frac{1}{\det(A)}\operatorname{adj}(A)

A^T = [a_{ji}]

Choose an operation, set the matrix size, and enter the visible cells. The workspace only shows the inputs needed for that operation, then computes the matrix result, determinant, or invertibility status directly in the browser.

Addition and subtraction combine matching entries. Multiplication uses row-by-column dot products. Transpose swaps rows and columns. Determinants use the standard 1x1, 2x2, and 3x3 formulas. Inverse mode first computes $\det(A)$ and only returns $A^{-1}$ when the determinant is non-zero.

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