Question 3

A matrix can be obtained from the identity matrix $I$ using elementary row transformations if and only if it is non-singular (i.e., its determinant is non-zero).

Evaluating the determinants of the given options:

(A) $|A| = 0$ as all rows are identical.

(B) $|B| = 1(3 - 8) - 1(2 - 4) + 1(4 - 3) = -5 + 2 + 1 = -2$ $\neq 0$.

(C) $|C| = 1(24 - 20) - 1(16 - 8) + 1(10 - 6) = 4 - 8 + 4 = 0$.

(D) $|D| = 1(3 - 4) - 1(-3 - 0) + 1(-2 - 0) = -1 + 3 - 2 = 0$.

Since only matrix (B) is non-singular, it is the only one that can be obtained from the $3 \times 3$ identity matrix via elementary row transformations.