Question

For the matrix `X = [(0, 1, 1),(1, 0, 1),(1, 1, 0)], (X^2 - X)` is ______.

Options

• 2I

• 3I

• I

• 5I

Answer 1

For the matrix `X = [(0, 1, 1),(1, 0, 1),(1, 1, 0)], (X^2 - X)` is 2I.

Explanation:

Here `X^2 = [(0, 1, 1),(1, 0, 1),(1, 1, 0)][(0, 1, 1),(1, 0, 1),(1, 1, 0)]`

`\implies X^2 = [(2, 1, 1),(1, 2, 1),(1, 1, 2)]`

`\implies X^2 - X = [(2, 0, 0),(0, 2, 0),(0, 0, 2)]`

= `2[(1, 0, 0),(0, 1, 0),(0, 0, 1)]`

= 2I