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Let P= [ array lll 1 & 1 & 0 0 & 1 & 0 0 & 1 & 1 array ] and Q be an orthogonal matrix of order 3 3 . Let A=P²⁰¹⁸ and B=Q P Q^T , then which of the following is/are correct?

Options

  1. ATrace of matrix A is 3
  2. BQ^T B²⁰¹⁸ Q=A
  3. Cdet (B^5 )=1
  4. Ddet ( adj (A))= det ( adj (B))

Correct answer

D. det ( adj (A))= det ( adj (B))

Step-by-step solution

p^n= [ array lll 1 & n & 0 0 & 1 & 0 0 & n & 1 array ] and B^n=Q P^n Q^T det (A)=1 and det (B)=1

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