Question

If `A = [(0, a),(0, 0)]`, then A¹⁶ is ______.

Options

• Unit matrix

• Null matrix

• Diagonal matrix

• Skew matrix

Answer 1

If `A = [(0, a),(0, 0)]`, then A¹⁶ is null matrix.

Explanation:

Given `A = [(0, a),(0, 0)]`

A² = A · A

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

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

A⁴ = A² · A²

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

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

Similarly

A¹⁶ = (A⁴)⁴

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

A¹⁶ is null matrix.