Let A be orthogonal. and consider:

(A^t A)_{i,j}

this is the dot product of the i-th col and j-th col of A, hence as A^t=A^{-1}:

(A^t A)_{i,j} = 1, if i = j

(A^t A)_{i,j} = 0, if i != j

The converse is not true, Consider any orthogonal matrix A, then B=2A has theIs this true for the converse of this statement as well? Justify your answer.

given property but:

B^t B = 4 I.

RonL