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If A= [ array lll 2 & 0 & 0 0 & 3 & 0 0 & 0 & 4 array ] , then which of the following statements are correct? 1. A^n will always be singular for any positive integer n . 2. A ^ n will always be a diagonal matrix for any positive integer n . 3. A ^ n will always be a symmetric matrix for any positive integer n . Select the correct answer using the code given below:

Options

  1. A1 and 2 only
  2. B2 and 3 only
  3. C1 and 3 only
  4. D1, 2 and 3

Correct answer

B. 2 and 3 only

Step-by-step solution

Given A= [ array lll 2 & 0 & 0 0 & 3 & 0 0 & 0 & 4 array ] is a non-zero diagonal matrix So A^n is also non-zero diagonal matrix for any n N and diagonal elements of A are positive so A^n is also symmetric thus the statements 2 and 3 are correct.

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