If A is an adjoint operator on H=K2 and  for x=(x(1), x(2)), we define A(x)=(x(1)-x(2), x(1)+x(2)), how do we derive that A*(x) = (x(1)+x(2), -x(1)+x(2))?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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If A is an adjoint operator on H=K2 and  for x=(x(1), x(2)), we define A(x)=(x(1)-x(2), x(1)+x(2)), how do we derive that

A*(x) = (x(1)+x(2), -x(1)+x(2))?

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