Question

If A = `[(0, 1),(0, 0)]`, then A²⁰²³ is equal to ______.

Options

• `[(0, 1),(0, 0)]`

• `[(0, 2023),(0, 0)]`

• `[(0, 0),(0, 0)]`

• `[(2023, 0),(0, 2023)]`

Answer 1

If A = `[(0, 1),(0, 0)]`, then A²⁰²³ is equal to `underlinebb([(0, 0),(0, 0)])`.

Explanation:

Given:

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

A² = A.A

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

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

A³ = A².A

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

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

Similarly, A²⁰²³ = `[(0, 0),(0, 0)]`