Suppose we have a Matrix N, what does it mean if $N^T \cdot N =1$? My Thought was that either they are orthogonal or perhaps that N is orthogonal and hence $N^T=N^{-1}$ so we get $N^T N=N^{-1}N=I$ because if we multiply $ N^T \cdot N=1$ by I we get $ N^T \cdot N \cdot I=1 \cdot I=NN^T=I$.
Note that "I" here of course is the identity matrix. Is this reasoning okay?
Thanks in advance!