Nilpotent Matrix – Definition, Properties and Example

Any square matrix [A] is said to be a Nilpotent matrix if it satisfies the condition [Ak] = 0 and [Ak-1] ≠ 0 for some positive integer value of k. Then the least value of such positive integer k is called the index (or degree) of nilpotency.

Involutory matrix – Definition, Examples and its properties

An Involutory matrix is simply a square matrix that when multiplied itself will result in an identity matrix. In other words, mathematically we can define an involutory matrix as: If A is a square matrix then matrix A will be called an involutory matrix if and only if it satisfies the condition   A2 = I. Where I is n x n identity matrix.