Question

Hi, I really need help with these True/False questions:

(a) If three vectors in R^3 are orthonormal then they form a basis in R^3.
(b) If Q is square orthogonal matrix such that Q^2018 = I then Q^2017 = Q^T.
(c) If B is square orthogonal matrix then B^−1 = B^T.
(d) If for some basis {a_1, a_2} for vector b one has b = xa_1 +ya_2 then magnitude(b) = sqrt(x^2 + y^2).
(e) If columns of matrix A are orthogonal then rows of A are independent.
(f) Row operations do not change the determinant of a matrix.
(g) If det(2A) = det(3A) then A is not invertible.
(h) If det(A) = det(A^-1) then A = I.
(i) There are no matrix A such that det A^−1 = 0.

Thanks in advance!