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.