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Question
The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:
`[(0, 1 + 2"i", "i" - 2),(-1 - 2"i", 0, -7),(2 - "i", 7, 0)]`
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Solution
Let A = `[(0, 1 + 2"i", "i" - 2),(-1 - 2"i", 0, -7),(2 - "i", 7, 0)]`
∴ AT = `[(0, -1 - 2"i", 2 - "i"),(1 + 2"i", 0, 7),("i" - 2, -7, 0)]`
∴ AT = `-[(0, 1 + 2"i", "i" - 2),(-1 - 2"i", 0, -7),(2 - "i", 7, 0)]`
∴ AT = – A, i.e., A = –AT
∴ A is a skew-symmetric matrix.
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