Construct a 2 $\times$ 2 matrix whose elements a_ij are given by

(i) a_ij = 2i - j

(ii) a_ij = i.j

(i) Given a_ij = 2i - j,

∴ a₁₁ = 2(1) - 1 = 1, a₁₂ = 2(1) - 2 = 0,
    a₂₁ = 2(2) - 1 = 3, a₂₂ = 2(2) - 2 = 2.

Hence, the required matrix =$\begin{bmatrix} 1 & 0 \ 3 & 2 \end{bmatrix}$.

(ii) Given a_ij = i.j,

∴ a₁₁ = 1.1 = 1, a₁₂ = 1.2 = 2,
    a₂₁ = 2.1 = 2, a₂₂ = 2.2 = 4.

Hence, the required matrix =$\begin{bmatrix} 1 & 2 \ 2 & 4 \end{bmatrix}$.