Question

If A = [a_ij] is a square matrix of order 2 such that a_ij = `{(1","  "when i" ≠ "j"),(0","  "when"  "i" = "j"):},` then A² is ______.

Options

• `[(1,0),(1,0)]`

• `|(1,1),(0,0)|`

• `|(1,1),(1,0)|`

• `[(1,0),(0,1)]`

Answer 1

If A = [a_ij] is a square matrix of order 2 such that a_ij = `{(1","  "when i" ≠ "j"),(0","  "when"  "i" = "j"):},` then A² is `underlinebb([(1,0),(0,1)])`.

Explanation:

a_ij = `{{:(1",", i ≠ j),(0",", i = j):},`

then A = `[(0, 1),(1, 0)]`

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