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If  then the matrix A is a/an

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  1. Singular matrix
  2. involuntary matrix
  3. Nilpotent matrix
  4. Idempotent matrix

Answer (Detailed Solution Below)

Option 2 : involuntary matrix
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Detailed Solution

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Concept:

Singular Matrix: Any square matrix of order n is said to be singular if |A| = 0.

Involuntary Matrix: Any square matrix of order n is said to be an involuntary matrix if A2 = I, where I is the identity matrix of order n.

Nilpotent Matrix: Any square matrix of order n is said to be nilpotent matrix if there exist least positive integer m such that Am = O, where O is the null matrix of order n.

Idempotent Matrix: Any square matrix of order n is said to be an idempotent matrix if A2 = A.

Calculation:

Given:

Hence, A is an involuntary matrix as A2 = I.

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