Construct a 2 × 2

We are given that a_ij is given as

We need to construct a 2 × 2 matrix A defined as A = [a_ij].

Since, this is a 2 × 2 matrix where A = [a_ij], we know

Number of rows = 2

Number of columns = 2

∴, i = 1, 2

& j = 1, 2

First, put i = 1 and j = 1 in a_ij, here i = j.

For i = j,

a_ij = (i + j)²

So,

a₁₁ = (1 + 1)²

⇒ a₁₁ = 2²

⇒ a �₁₁ = 4

Put i = 1 and j = 2 in a_ij, here i ≠ j.

For i ≠ j,

So,

Put i = 2 and j = 1 in a_ij, here i ≠ j.

For i ≠ j,

So,

Put i = 2 and j = 2 in a_ij, here i = j.

For i = j,

a_ij = (i + j)²

So,

a₂₂ = (2 + 2)²

⇒ a₂₂ = 4²

⇒ a₂₂ = 16

Thus, we get