Question

Find the matrix A², where A = [a_ij] is a 2 × 2 matrix whose elements are given by a_ij = maximum (i, j) − minimum (i, j): 

Options

• `[(0, 0),(0, 0)]`

• `[(0, 1),(1, 0)]`

• `[(1, 0),(0, 1)]`

• `[(1, 1),(1, 1)]`

Answer 1

`bb([(1, 0),(0, 1)])` 

Explanation:

Given for matrix A = [a_ij]_2×2

We have a_ij = max(i, j) − min (i, j)

∴ a₁₁ = 1 − 1 = 0

a₁₂ = 2 − 1 = 1

a₂₁ = 2 − 1 = 1

a₂₂ = 2 − 2 = 0

∴ A = `[(0, 1),(1, 0)]`

Now, A² = `[(0, 1),(1, 0)] [(0, 1),(1, 0)] = [(1, 0),(0, 1)]`