Linear Algebra

Matrix Multiplication Calculator

Multiply matrices A and B to produce the product matrix AB while verifying dimensional compatibility.

matrix multiplicationproductlinear algebra
Matrix Multiplication

Multiply compatible matrices (A · B).

Result size
2 × 2
Product matrix
4	4
10	8

Matrix product

(AB)_{ij} = Σₖ A_{ik} B_{kj}

Each entry in the product is the dot product of a row of A with a column of B. The output matrix adapts to the valid shape.

How to use

  1. Enter matrix A and matrix B with rows separated by new lines.
  2. Ensure the number of columns in A equals the number of rows in B.
  3. Review the resulting product matrix and its size.

Example

Input: A = [[1,2],[3,4]], B = [[2,0],[1,2]]

Output: AB = [[4,4],[10,8]]

Student-friendly breakdown

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Deep dive & study plan

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Under the hood, the calculator leans on each entry in the product is the dot product of a row of a with a column of b. the output matrix adapts to the valid shape.—that’s why we surface the full expression (“(AB)_{ij} = Σₖ A_{ik} B_{kj}”) directly above the interactive widget. When you embed that formula inside H2s or supporting paragraphs, you help both humans and crawlers understand what entity the page represents.

Execution matters as much as the math. Follow the built-in procedure: Step 1: Enter matrix A and matrix B with rows separated by new lines. Step 2: Ensure the number of columns in A equals the number of rows in B. Step 3: Review the resulting product matrix and its size.. Each numbered instruction is short enough to scan on mobile but descriptive enough to satisfy Google’s Helpful Content guidelines. Encourage students to jot down units, double-check signs, and compare answers with the Example card to build confidence.

The Example section itself is packed with semantic clues: “A = [[1,2],[3,4]], B = [[2,0],[1,2]]” leading to “AB = [[4,4],[10,8]].” Pepper similar narratives throughout your copy (and internal links from related guides) so canonical search intents are answered without pogo-sticking back to Google.

Quick retention checklist

  • Speak the formula aloud (or annotate it) so the relationships stick.
  • Write each step in your own words and compare with the numbered list above.
  • Swap in new numbers for the Example to make sure the calculator (and your logic) handles edge cases.
  • Link out to at least two related calculators to keep readers exploring your topical hub.

FAQ & notes

Can I multiply non-square matrices?

Absolutely. As long as the inner dimensions match, the output size adapts to the inputs.

How are results formatted?

Results appear in a preformatted grid that you can copy into spreadsheets or documentation.

What formula does the Matrix Multiplication Calculator use?

Each entry in the product is the dot product of a row of A with a column of B. The output matrix adapts to the valid shape.

How do I use the Matrix Multiplication Calculator?

Enter matrix A and matrix B with rows separated by new lines. Ensure the number of columns in A equals the number of rows in B. Review the resulting product matrix and its size.