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There is an example of this question in the book but I cannot understand the part where it says 2AT = 2[2AT]T. Everything else I understand. (T means Transpose)

Suppose a square matrix A satisfies A = 2AT. Show that necessarily A=0.

A =

**2AT = 2[2AT]T**= 2[2(AT)T] = 4A

3A = 0

A=1/3(3A) = 1/3(0) = (0)

Thanks!