R * RR

$\large \text{If you will notice when } R\times R \text{ happens, the result is also R}$

$$

$\large \text{In order to lessen the possible numbers, we are only concerned with the ones digit of the number}$

$\large \begin{matrix} 1 & \times & 1 & = & \boxed { 1 } \\ 2 & \times & 2 & = & \boxed { 4 } \\ 3 & \times & 3 & = & \boxed { 9 } \\ 4 & \times & 4 & = & 1\boxed { 6 } \\ 5 & \times & 5 & = & 2\boxed { 5 } \\ 6 & \times & 6 & = & 3\boxed { 6 } \\ 7 & \times & 7 & = & 4\boxed { 9 } \\ 8 & \times & 8 & = & 6\boxed { 4 } \\ 9 & \times & 9 & = & 8\boxed { 1 } \end{matrix}$

$\large \text{So, given the numbers 1 to 9 only 1, 5, and 6 fits the criteria}$

$$

$\large \begin{matrix} RR & \times & R & = & XYZ \\ 11 & \times & 1 & = & 11 \\ 55 & \times & 5 & = & 275 \\ 66 & \times & 6 & = & 396 \end{matrix}$

$$

$\large \text{And from these, we can see that only R = 5 and R = 6 satisfies the cryptogram.}$

two solutions are: 5x 55= 275

and 6 x 66 =396