Question

If A = `[(0,0,0),(0,0,0),(0,1,0)]` then A is ____________.

Options

• none of these

• a nilpotent matrix

• an idempotent matrix

• an invertible matrix

Answer 1

If A = `[(0,0,0),(0,0,0),(0,1,0)]` then A is a nilpotent matrix.

Explanation:

A Nilpotent matrix is a square matrix A with Aⁿ = 0, where n is a positive integer. For a Nilpotent Matrix, the determinant and trace are both always zero. Determinant (A) = 0 and trace(A) = 0 for the given matrix "A."