Mark each of the following True or False.

Question

___ a. All vectors in an orthogonal basis have length 1.
___ b. A square matrix is orthogonal if its column vectors are orthogonal.
___ c. If A^T is orthogonal, then A is orthogonal.
___ d. If A is an n*n symmetric orthogonal matrix then A^2=I .
___ e. If A is an n*n symmetric matrix such that A^2=I, then A is orthogonal.
___ f. If A and B are orthogonal n*n matrices, then AB is orthogonal.
___ g. Every orthogonal matrix has nullspace {0}
___ h. Every n*k matrix A has a factorization A=QR, where the column vectors of Q form an orthonormal set and R is an invertible k*k matrix.