Prove the following:

a) (A^T)^T=A

b) (A + B)^T= A^T + B^T

c)(AB)^T=(B^T)(A^T)

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- Sep 29th 2009, 10:08 AMamm345Matrices- Transpose Help
Prove the following:

a) (A^T)^T=A

b) (A + B)^T= A^T + B^T

c)(AB)^T=(B^T)(A^T) - Sep 29th 2009, 10:21 AMpomp
I'll set you off on the first and then you should see how to do the rest.

Use (i,j) notation: $\displaystyle A = \sum a_{ij}$.

Then by definition: $\displaystyle A^T = \sum a_{ji}$.

So, $\displaystyle (A^T)^T = \left(\sum a_{ji}\right)^T = \sum a_{ij} = A $.

Hope this helps,

pomp.