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Question
If A = `[(0, 1 + 2"i", "i" - 2),(-1 - 2"i", 0, -7),(2 - "i", 7, 0)]` where i = `sqrt(-1)` Prove that AT = – A
Sum
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Solution
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)] ...(1)`
and – A = `-[(0,1 + 2"i","i" - 2),(-1 - 2"i", 0, -7),(2 - "i",7, 0)]`
= `[(0,-1 - 2"i",2 - "i"),(1 + 2"i", 0, 7),("i" - 2, -7, 0)] ...(2)`
From (1) and (2),
∴ AT = – A.
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