Solving Linear Algebra Proof: A = 0

[vg19]

Hi,

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!

 

[iNCREDiBLE]

They are just using the assumption $A = 2A^T$ in that step.

 

[vg19]

I think I get it. So basically are they doing that step to get rid of the Transpose so A will be alone, and then can be isolated?

Thanks

 

[iNCREDiBLE]

I think I get it. So basically are they doing that step to get rid of the Transpose so A will be alone, and then can be isolated?

Thanks

Yes, you could say that.