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Question
If A is a symmetric matrix and n ∈ N, write whether An is symmetric or skew-symmetric or neither of these two.
Solution
`If A is a symmetric matrix, then A^T = A .`
\[Now, \]
`( A^n)^T = ( A^T )^n [ "for" all n ∈ N]`
Hence, is a symmetric matrix.` ( A)^n `
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