Question

If A is a matrix, such that, A^k = 0, for positive integer k, then, A is known as Nilpotent matrix.

(a) True

(b) False

I have been asked this question in quiz.

My doubt stems from Canonical Form or Sum of Squares Form in chapter Eigen Values and Eigen Vectors of Engineering Mathematics

Answer 1

The correct choice is (a) True

Explanation: For a matrix A, A^k+1 = A, where k is a positive integer is known as periodic matrix.

Whereas, if A^2 = A, i.e. k=1, then it is known as idempotent matrix and if A^k = 0, then it is known as Nilpotent matrix.