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If A= [ array ccc 0 & 3 & 4 -3 & 0 & 5 -4 & -5 & 0 array ] , then which one of the following statements is correct?

Options

  1. AA ^2 is symmetric matrix with det ( A ^2 )=0
  2. BA^2 is symmetric matrix with det (A^2 ) 0
  3. CA ^2 is skew-symmetric matrix with det ( A ^2 )=0
  4. DA ^2 is skew-symmetric matrix with det ( A ^2 ) 0

Correct answer

A. A ^2 is symmetric matrix with det ( A ^2 )=0

Step-by-step solution

Since the matrix A is skew symmetric of order 3 (odd) So, |A|=0 and A ^2 is symmetric matrix Now |A^2 |=|A|^2=0 Similarly, |A^3 |=0, |A^4 |=0 Hence |4 ~A ^4 |- |3 ~A ^3 |+ |2 ~A ^2 |-| A |+(-1)^3 | I ₃ |=-1

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