Matrix Addition & Subtraction Calculator

Free Client-Side Step-by-Step

Add, subtract matrices, and perform scalar multiplication with step-by-step solutions. Supports A+B, A−B, cA, and linear combinations aA+bB. 100% client-side—no data sent to servers. Enter matrices up to 10×10 or use quick examples.

Operation
Matrix A
×
One row per line, space separated
Matrix B
One row per line, space separated
Quick Examples
Result
Select an operation and enter matrices to see the result.
Computation Steps
Detailed computation steps will appear here.

Exam-Style Practice

About This Matrix Addition Tool & Methodology

This matrix addition calculator performs element-wise operations using standard linear algebra rules. All computations run client-side in your browser—no matrices are sent to any server. Supports A+B, A−B, scalar multiplication cA, and linear combinations aA+bB with step-by-step solutions up to 10×10.

Authorship & Expertise

  • Author: Anish Nath
  • Background: Math and developer tools for education
  • Standards: Standard linear algebra (element-wise operations)

Trust & Privacy

  • Privacy: All calculations run locally; no data stored
  • Client-side: Your matrices never leave your device
  • Support: @anish2good

Matrix Addition & Subtraction: FAQ

How do you add and subtract matrices?

Addition and subtraction are element-wise and require the same dimensions. For result C, cij = aij ± bij. Addition is commutative and associative.

What is scalar multiplication and a linear combination?

Scalar multiplication multiplies each entry by a constant c. Linear combinations have the form aA + bB with matching dimensions, fundamental for many linear algebra applications.

What sizes are supported?

This tool supports matrices up to 10×10 and shows element-wise steps for A+B, A−B, cA, and aA+bB.

Can I practice with exam-style questions?

Yes. Scroll to the Exam-Style Practice section and choose Easy (2×2), Medium (3×3), or Hard (linear combinations). Generate problems, enter answers, and get instant scoring with detailed solutions.

What are common mistakes in matrix addition?

The most common errors are adding matrices of different dimensions (not allowed), forgetting to negate every entry in subtraction, and misapplying scalar multiplication to only some entries instead of all.

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