The number of all possible matrices of order $3 \times 2$ with each entry 1 or 2 is :

This tests the order of a matrix combined with the multiplication principle of counting.

Concept:

• A matrix of order $m \times n$ has exactly $m \cdot n$ entries.
• If each entry has k possible values, the number of distinct matrices is $k^{m \cdot n}$.

Why D is correct:

• Here $m \cdot n = 3 \times 2 = 6$ and $k = 2$, so $2^6 = 64$.

Why the distractors are wrong:

• A (6): counts only the number of entries, not the arrangements.
• B (16): equals $2^4$, mistaking the order for $2 \times 2$.
• C (24): a spurious product (e.g. $4!$ or $6 \times 4$), unrelated to the counting rule.