If \(A=[a_{ij}]\) is a \(2\times2\) matrix and \(a_{ij}=j\), what is \(A\)?

Correct answer: \(A=\begin{bmatrix}1 & 2 \\ 1 & 2\end{bmatrix}\)

By definition \(a_{ij}=j\) means each entry equals its column index. In a 2×2 matrix all entries in column 1 are 1 and all entries in column 2 are 2. Thus \(A=\begin{bmatrix}1&2\\1&2\end{bmatrix}\). Option B would correspond to \(a_{ij}=i\) (row index) and is therefore incorrect; options C and D do not follow the column-index rule either. Exam tip: write down the indices \(i,j\) for each position and substitute the rule to avoid sign/index errors.