CalcLibrary

Matrix Calculator

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

Examples

Add two 2x2 matrices

Quickly check row-by-row arithmetic for a basic sum.

Rechenart
Add
Rows
2
Columns
2
Matrix A
1,2;3,4
Matrix B
5,6;7,8
Result
6, 8 ; 10, 12
Status
Addition is defined because both matrices share the same shape.

Examples

Add two 2x2 matricesQuickly check row-by-row arithmetic for a basic sum.6, 8 ; 10, 12
Multiply 2x3 by 3x2A classic dimension-check case for intro linear algebra.58, 64 ; 139, 154
Find a 3x3 determinantUse a square matrix and confirm the determinant directly.19
Invert a 2x2 matrixSee the inverse and determinant together to confirm invertibility.0.6, -0.7 ; -0.2, 0.4

How It Works

Formula

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

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

det⁡[abcd]=ad−bc\det\begin{bmatrix} a & b \\ c & d \end{bmatrix} = ad - bc

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

AT=[aji]A^T = [a_{ji}]

Variables

A,BA, B

Input matrices

aij,bija_{ij}, b_{ij}

Entries in rows i and columns j

det⁡(A)\det(A)

Determinant of matrix A

A−1A^{-1}

Inverse of matrix A

ATA^T

Transpose of matrix A

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)\det(A) and only returns A−1A^{-1} when the determinant is non-zero.

Frequently Asked Questions

01What 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.
02When 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.
03When 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.
04Why 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.
05Does 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.

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