Matrices · 2.2.3
Multiplying two matrices
This standard asks students to multiply two matrices by combining rows of the first matrix with columns of the second, adding the products of matching entries. Multiplication is only possible when the number of columns in the first matrix equals the number of rows in the second, and the result has the outer order of the two matrices.
The official learning standard (2.2.3)
“Multiply two matrices.”
What it means
This standard asks students to multiply two matrices by combining rows of the first matrix with columns of the second, adding the products of matching entries. Multiplication is only possible when the number of columns in the first matrix equals the number of rows in the second, and the result has the outer order of the two matrices.
How it is examined
Matrix multiplication is tested in Paper 1 through short questions asking for the product of two small matrices, and in Paper 2 as part of larger structured questions that build up to finding an inverse matrix or solving simultaneous linear equations, where an incorrect multiplication step affects every later answer.
Worked example
Given A = [[2, 1], [3, 4]] and B = [[1, 0], [2, 5]], find AB.
- Multiply row 1 of A by column 1 of B: (2×1) + (1×2) = 2 + 2 = 4
- Multiply row 1 of A by column 2 of B: (2×0) + (1×5) = 0 + 5 = 5
- Multiply row 2 of A by column 1 of B: (3×1) + (4×2) = 3 + 8 = 11
- Multiply row 2 of A by column 2 of B: (3×0) + (4×5) = 0 + 20 = 20
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
Can I multiply any two matrices together?
No. Two matrices A and B can only be multiplied as AB if the number of columns in A equals the number of rows in B.
If this condition is not met, the multiplication AB is undefined, even though BA might still be possible.
Does AB always equal BA?
Generally no. Matrix multiplication is not commutative, so AB and BA are usually different, and one of them may not even be defined if the matrix orders do not match.
Always multiply in the exact order given in the question.
How do I know the order (size) of the product matrix?
The product matrix takes its number of rows from the first matrix and its number of columns from the second matrix. For an m×n matrix multiplied by an n×p matrix, the product is an m×p matrix.