How do you multiply two matrices?

Mathematics

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Answer

m×p

To multiply matrices A(m×n) and B(n×p), the number of columns in A must equal rows in B. Result is m×p. Each element C[i][j] = sum of (row i of A) × (column j of B). Example: [1,2; 3,4] × [5,6; 7,8] = [1×5+2×7, 1×6+2×8; 3×5+4×7, 3×6+4×8] = [19, 22; 43, 50]. Important: matrix multiplication is NOT commutative — A×B ≠ B×A in general.

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To multiply matrices A(m×n) and B(n×p), the number of columns in A must equal rows in B.

How do you multiply two matrices?
Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI Answer
To multiply matrices A(m×n) and B(n×p), the number of columns in A must equal rows in B. Result is m×p. Each element C[i][j] = sum of (row i of A) × (column j of B). Example: [1,2; 3,4] × [5,6; 7,8] = [1×5+2×7, 1×6+2×8; 3×5+4×7, 3×6+4×8] = [19, 22; 43, 50]. Important: matrix multiplication is NOT commutative — A×B ≠ B×A in general.