JAMB Mathematics 2023 Paper

Concept:Matrix multiplication: To find matrix $A$, multiply an unknown matrix $A$ by the given matrix, then compare each corresponding entry of the resulting product with the right-hand side matrix.Explanation:Let $A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$.Then multiplying by the given matrix gives:$$\begin{bmatrix} a & b \\ c & d \end{bmatrix} \begin{bmatrix} 0 & 1 \\ 2 & -1 \end{bmatrix} = \begin{bmatrix} 2b & a-b \\ 2d & c-d \end{bmatrix}$$This must equal $\begin{bmatrix} 2 & -1 \\ 1 & 0 \end{bmatrix}$.Comparing the entries gives four equations:$2b = 2$,$a - b = -1$,$2d = 1$,$c - d = 0$.Solve them:$b = \frac{2}{2} = 1$,$a - 1 = -1 \Rightarrow a = 0$,$d = \frac{1}{2}$,$c = d = \frac{1}{2}$.So the matrix $A$ is formed from these values.Answer:$$A = \begin{bmatrix} 0 & 1 \\ \frac{1}{2} & \frac{1}{2} \end{bmatrix}$$This corresponds to Option B.