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Question
The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:
`[(2, 5, 1),(-5, 4, 6),(-1, -6, 3)]`
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Solution
Let B = `[(2, 5, 1),(-5, 4, 6),(-1, -6, 3)]` ...(1)
∴ B' = `[(2, -5, -1),(5, 4, -6),(1, 6, 3)]` ...(2)
Also, –B' = `[(-2, 5, 1),(-5, -4, 6),(-1, -6, -3)]` ...(3)
From (1), (2) and (3),
neither B = B' nor B = - B'
∴ B is the neither symmetric nor skew-symmetric matrix.
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