ANSWER
The correct answer is D
EXPLANATION
We use the dimensions of a matrix to determine if the multiplication of any two given matrices is possible.
Option A
The dimensions are
[tex](1\times 2 \: ) \times ( \: 1 \times2)[/tex]
The inner products are not the same, so the matrix multiplication is not possible.
Option B
[tex](2 \times 1) \times (2 \times 2)[/tex]
The inner products are not the same so matrix multiplication is not possible.
Option C
[tex](2 \times 2) \times (1 \times 2)[/tex]
The inner products are not the same so matrix multiplication is not possible.
Option D
[tex](2 \times 1) \times (1 \times 2)[/tex]
The inner products are the same. Matrix multiplication is possible.
The resulting matrix will have dimension
[tex](2 \times 2)[/tex]
The correct answer is D
