Explanation

Matrix multiplication is not entry-by-entry.

Rule:
(A)(B) is defined only if:

• Columns of A = rows of B

Each entry is found by:

• Row × column multiplication

Order matters:
AB ≠ BA (usually)

Quiz

1. When is matrix multiplication defined?

2. Is matrix multiplication commutative?

3. What is used to compute each entry?

4. Do dimensions change?

5. Is AB always possible?

Answer Key

1. Matching dimensions

2. No

3. Row × column

4. Yes

5. No