Prove A Orthogonal $\Rightarrow$ |A|=+-1

[eyehategod]

Prove if A is orthogonal matrix, then |A|=+-1
A^{-1}=A^{T}
AA^{-1}=AA^{T}
I=AA^{T}
|I|=|AA^{T}|
1=|A|*|A^{T}|//getting to the next step is where i get confused. Why is |A|=|A^{T}|
1=|A|*|A|
1=|A|^{2}
+-1=|A|

 

[unplebeian]

I think there is an error in your question. For matrices to be orthogonal A_inverse= A_transpose.

Sorry I am not yet familiar with LATEX.

 

[morphism]

getting to the next step is where i get confused. Why is |A|=|A^{T}|

This is a standard result. You should probably find it in your textbook, or try to prove it yourself.