From the two matrices, find A'U B'.

Matrix B has 3 rows and 3 columns.  
The dimension of B is $\boxed{3 \times 3}$.

    $$
    B = \begin{pmatrix} 5 & 2 & 1 \\ \mathbf{4} & 7 & 6 \\ 13 & 9 & 12 \end{pmatrix}
    $$
    The element $b_{21}$ is $\boxed{4}$.
*   **B-(2)-(ii) $a_{22}$**

    $$
    A = \begin{pmatrix} 1 & 2 & 4 \\ 3 & \mathbf{7} & 8 \\ 11 & 13 & 10 \end{pmatrix}
    $$
    The element $a_{22}$ is $\boxed{7}$.

$$
2A = 2 \begin{pmatrix} 1 & 2 & 4 \\ 3 & 7 & 8 \\ 11 & 13 & 10 \end{pmatrix} = \begin{pmatrix} 2 & 4 & 8 \\ 6 & 14 & 16 \\ 22 & 26 & 20 \end{pmatrix}
$$

$$
2A+B = \begin{pmatrix} 2+5 & 4+2 & 8+1 \\ 6+4 & 14+7 & 16+6 \\ 22+13 & 26+9 & 20+12 \end{pmatrix}
$$

$$
2A+B = \boxed{\begin{pmatrix} 7 & 6 & 9 \\ 10 & 21 & 22 \\ 35 & 35 & 32 \end{pmatrix}}
$$

$$
A \times B = \begin{pmatrix} (1)(5)+(2)(4)+(4)(13) & (1)(2)+(2)(7)+(4)(9) & (1)(1)+(2)(6)+(4)(12) \\ (3)(5)+(7)(4)+(8)(13) & (3)(2)+(7)(7)+(8)(9) & (3)(1)+(7)(6)+(8)(12) \\ (11)(5)+(13)(4)+(10)(13) & (11)(2)+(13)(7)+(10)(9) & (11)(1)+(13)(6)+(10)(12) \end{pmatrix}
$$

$$
A \times B = \begin{pmatrix} 5+8+52 & 2+14+36 & 1+12+48 \\ 15+28+104 & 6+49+72 & 3+42+96 \\ 55+52+130 & 22+91+90 & 11+78+120 \end{pmatrix}
$$

$$
A \times B = \boxed{\begin{pmatrix} 65 & 52 & 61 \\ 147 & 127 & 141 \\ 237 & 203 & 209 \end{pmatrix}}
$$

$$
A^T = \boxed{\begin{pmatrix} 4 & 1 \\ 3 & -9 \\ 2 & 6 \end{pmatrix}}
$$

$$
B^T = \boxed{\begin{pmatrix} 5 & 1 & -3 \\ 2 & 3 & 1 \end{pmatrix}}
$$