What are the conditions for m row n column matrix A and p row q column matrix B to be multiplied?

Question

Options

• Am=p. n=q
• Bn=p
• Cm=n
• Dp=q

• A
  3% (2)
• B
  78% (46)
• C
  8% (5)
• D
  10% (6)

Explanation

For matrix multiplication A x B, the number of columns in A must equal the number of rows in B, making n = p the required condition. This is because each entry in the product is computed as a dot product between a row of A (which has n elements) and a column of B (which has p elements), so those lengths must match.

Option A is wrong because requiring m = p and n = q would mean both matrices have the same dimensions, which is far too restrictive and unrelated to why multiplication works. Option C is wrong because m = n simply means A is a square matrix, which says nothing about compatibility with B. Option D is wrong because p = q means B is square, which is similarly irrelevant to whether the multiplication can proceed.

Memory tip: Write out the dimensions side by side as (m x n)(p x q) and think of the two middle numbers - the "inner" pair (n and p) must match, and the outer pair (m and q) gives you the dimensions of the result.

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