Matrix Calculator – Solve Matrices Online Easily

Intro

The Matrix Calculator online is a versatile tool that helps users perform matrix operations quickly and accurately. Matrices are widely used in mathematics, computer science, engineering, physics, economics, and data analysis, but solving them manually can be time-consuming and error-prone.

This tool allows you to perform operations like matrix addition, subtraction, multiplication, determinants, inverses, transposes, and more with just a few clicks. Whether you’re a student working on linear algebra problems, an engineer dealing with transformations, or a data scientist working with equations, the Matrix Calculator online makes solving matrices simple and efficient.

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Formula / Working

The calculator is based on the standard rules of matrix algebra:

1. Matrix Addition/Subtraction:
   If A=[aij]A = [a_{ij}]A=[aij​] and B=[bij]B = [b_{ij}]B=[bij​] are two matrices of the same size:

A+B=[aij+bij],A−B=[aij−bij]A + B = [a_{ij} + b_{ij}], \quad A – B = [a_{ij} – b_{ij}]A+B=[aij​+bij​],A−B=[aij​−bij​]

2. Matrix Multiplication:
   If AAA is m×nm \times nm×n and BBB is n×pn \times pn×p:

C=A×B,cij=∑k=1naik⋅bkjC = A \times B, \quad c_{ij} = \sum_{k=1}^{n} a_{ik} \cdot b_{kj}C=A×B,cij​=k=1∑n​aik​⋅bkj​

3. Determinant (2×2 Example):

det(A)=ad−bc\text{det}(A) = ad – bcdet(A)=ad−bc

4. Inverse of a Matrix:
   If AAA is invertible,

A−1=1det(A)⋅adj(A)A^{-1} = \frac{1}{\text{det}(A)} \cdot \text{adj}(A)A−1=det(A)1​⋅adj(A)

5. Transpose of a Matrix:

AT=[aji]A^T = [a_{ji}]AT=[aji​]

The calculator applies these formulas automatically based on the selected operation.

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Step-by-Step Usage

Using the Matrix Calculator online is simple:

1. Open the tool on your device.
2. Select the size of your matrix (e.g., 2×2, 3×3, 4×4).
3. Enter the values in the matrix cells.
4. Choose the operation (addition, multiplication, determinant, inverse, etc.).
5. Click Calculate to get results instantly.
6. (Optional) Reset and enter new matrices for more calculations.

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Examples

Example 1: Matrix Addition

A=[1234],B=[5678]A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}, \quad B = \begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix}A=[13​24​],B=[57​68​] A+B=[1+52+63+74+8]=[681012]A + B = \begin{bmatrix} 1+5 & 2+6 \\ 3+7 & 4+8 \end{bmatrix} = \begin{bmatrix} 6 & 8 \\ 10 & 12 \end{bmatrix}A+B=[1+53+7​2+64+8​]=[610​812​]

✅ Result: [681012]\begin{bmatrix} 6 & 8 \\ 10 & 12 \end{bmatrix}[610​812​]

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Example 2: Determinant of a 2×2 Matrix

A=[4638]A = \begin{bmatrix} 4 & 6 \\ 3 & 8 \end{bmatrix}A=[43​68​] det(A)=(4)(8)−(6)(3)=32−18=14\text{det}(A) = (4)(8) – (6)(3) = 32 – 18 = 14det(A)=(4)(8)−(6)(3)=32−18=14

✅ Result: Determinant = 14

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Example 3: Matrix Multiplication

A=[1234],B=[2012]A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}, \quad B = \begin{bmatrix} 2 & 0 \\ 1 & 2 \end{bmatrix}A=[13​24​],B=[21​02​] A×B=[(1×2+2×1)(1×0+2×2)(3×2+4×1)(3×0+4×2)]A \times B = \begin{bmatrix} (1 \times 2 + 2 \times 1) & (1 \times 0 + 2 \times 2) \\ (3 \times 2 + 4 \times 1) & (3 \times 0 + 4 \times 2) \end{bmatrix}A×B=[(1×2+2×1)(3×2+4×1)​(1×0+2×2)(3×0+4×2)​] =[44108]= \begin{bmatrix} 4 & 4 \\ 10 & 8 \end{bmatrix}=[410​48​]

✅ Result: [44108]\begin{bmatrix} 4 & 4 \\ 10 & 8 \end{bmatrix}[410​48​]

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FAQs

Q1. What is a Matrix Calculator?
It’s an online tool that solves matrix operations like addition, multiplication, determinants, and inverses.

Q2. Can it handle large matrices?
Yes, the calculator can handle multiple sizes (2×2, 3×3, 4×4, and more depending on the tool).

Q3. Is the Matrix Calculator free?
Yes, it’s completely free and works online without downloads.

Q4. Who can use this tool?
Students, teachers, engineers, programmers, and researchers.

Q5. Does it work on mobile devices?
Yes, it’s mobile-friendly and works on any browser.