JAMB Mathematics 2022 Paper

Concept:Matrix multiplication is possible when the number of columns in the first matrix equals the number of rows in the second matrix.Explanation:Matrix $A$ has order $3 \times 2$, and matrix $B$ has order $2 \times 2$.Because the inner dimensions match, the product $AB$ exists and will have order $3 \times 2$.Now compute each entry of $AB$ by multiplying corresponding row elements of $A$ with column elements of $B$ and adding the products.$$AB = \begin{pmatrix} (2 \cdot 3)+(1 \cdot 4) & (2 \cdot 2)+(1 \cdot 2) \\ (2 \cdot 3)+(3 \cdot 4) & (2 \cdot 2)+(3 \cdot 2) \\ (1 \cdot 3)+(2 \cdot 4) & (1 \cdot 2)+(2 \cdot 2) \end{pmatrix}$$Simplify each term:$$AB = \begin{pmatrix} 6+4 & 4+2 \\ 6+12 & 4+6 \\ 3+8 & 2+4 \end{pmatrix} = \begin{pmatrix} 10 & 6 \\ 18 & 10 \\ 11 & 6 \end{pmatrix}$$This matches option D.Answer:$$AB = \begin{pmatrix} 10 & 6 \\ 18 & 10 \\ 11 & 6 \end{pmatrix}$$So the correct option is D.