Question

If square matrix a is orthogonal, then prove that its inverse is also orthogonal.

Answer 1

We have `A A^(T)=I`
Now, `A^(-1) (A^(-1))^(T)=A^(-1) (A^(T))^(-1)=(A^(T)A)^(-1)=I^(-1)=I`
Thus, `A^(-1)` is orthonal.