NDA Mathematics Question (2025) — Solution

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