the counter example is matrix with first row (1,0,0) second row(0,0,2) third row (0,2,0) the matrix has eigenvalue 1,2i and -2i as rotational is orthgonal, so its eigenvalue must has modulus 1.

so the above matrix is not rotation matrix .

the counter example is matrix with first row (1,0,0) second row(0,0,2) third row (0,2,0) the matrix has eigenvalue 1,2i and -2i as rotational is orthgonal, so its eigenvalue must has modulus 1.

so the above matrix is not rotation matrix .