Question

If A = `[(0, 1 + 2"i", "i" - 2),(-1 - 2"i", 0, -7),(2 - "i", 7, 0)]` where i = `sqrt(-1)` Prove that A^T = – A

Answer 1

A = `[(0, 1 + 2"i", "i" - 2),(-1 - 2"i", 0, -7),(2 - "i", 7, 0)]` 

∴ A^T = `[(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),

∴ A^T = – A.