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Multiply square matrices with the row-times-column rule: C[i,j] = row i of A dotted with column j of B. Each entry's dot product is shown.
Row-times-column 2×2/3×3 products with each entry worked.
C[i,j] = Σₖ A[i,k]·B[k,j]
| Symbol | Meaning |
|---|---|
| AB | Product matrix (note: AB ≠ BA) |
[1,2;3,4]×[5,6;7,8]: C[1,1] = 1·5+2·7 = 19 → full result [19,22;43,50].
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Generally no — matrix multiplication is not commutative.
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Content updated: September 2026