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If A = pmatrix x & y & z y & z & x z & x & y pmatrix where x , y , z are integers, is an orthogonal matrix, then what is A^2 equal to?

Options

  1. ANull matrix
  2. BIdentity matrix
  3. CA
  4. D-A

Correct answer

B. Identity matrix

Step-by-step solution

Given the matrix A = pmatrix x & y & z y & z & x z & x & y pmatrix . The transpose of A is given by: A^T = pmatrix x & y & z y & z & x z & x & y pmatrix We can observe that A^T = A , which means A is a symmetric matrix. It is given that A is an orthogonal matrix. By the definition of an orthogonal matrix, we have: A A^T = I Substituting A^T = A into the above equation, we get: A A = I A^2 = I Thus, A^2 is equal to the identity matrix. Answer: Identity matrix

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