Match each type of matrix with all these descriptions that could fit:
(i) Can be multiplied by its transpose to make a 1 × 1 matrix,
(ii) Is similar to the 3 × 3 matrix of all zeros,
(iii) Can represent a linear map from R3 to R2 that is not onto,
(iv) Can represent an isomorphism from R3 to P2.
(a) a 2 × 3 matrix whose rank is 1
(b) a 3 × 3 matrix that is nonsingular
(c) a 2 × 2 matrix that is singular
(d) an n × 1 column vector