2. There are 4 cards each of red and blue, and each color of cards is marked with the numbers $1,2,3,4$. Arrange all 8 cards into a 2-row, 4-column matrix, requiring that cards with the same number are in the same column. The number of different arrangements is $(\quad)$.
(A) $\left(\mathrm{A}_{4}^{4} \mathrm{~A}_{4}^{4}\right)^{2}$
(B) $\mathrm{A}_{4}^{4}\left(\mathrm{~A}_{2}^{2}\right)^{4}$
(C) $\left(\mathrm{A}_{4}^{4} A_{2}^{2}\right)^{2}$
(D) $\mathrm{A}_{2}^{2}\left(\mathrm{~A}_{4}^{4}\right)^{4}$
2. B.

First, merge 2 cards with the same number into 1 card, resulting in 4 "large" cards. Arrange all of them, there are $A_{4}^{4}$ ways. Then, exchange the positions of the 2 cards in the same column, there are $\left(\mathrm{A}_{2}^{2}\right)^{4}$ ways. Therefore, there are $\mathrm{A}_{4}^{4}\left(\mathrm{~A}_{2}^{2}\right)^{4}$ arrangements.