Question

13 and 31 are mirror images of each other and their squares are 169 and 196 and they are also mirror images give 3 more numbers like this

Answer 1

Mirror Image of 13 is 31.

Now,
Square  of 13 = 169
∴ Square  of 31 = 961

We need to find such three numbers.

a) Mirror image of  12 is 21.
Square  of 12 = 144  
Square  of 21 = 441

Like this we can find more numbers.

Answer 2

As mentioned in another answer 12 is such a number.
I will give you 5 more numbers like this:

   Number       Reverse       Sqr of Number       Sqr of Reverse
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1)  102                201                 10404                       40401
2) 103                301                 10609                       90601
3) 112                 211                  12544                       44521
4) 113                 311                  12769                       96721
5) 122               221                  14884                       48841


It becomes easy to generate such numbers if you know a little bit of computer programming. You can write a code in Java to generate such numbers. I can provide more such numbers if you want. Or better can discuss the code I wrote to generate such numbers.