Magical solution to finding square of a two digit integer.

Maybe no one knows that there is a different way to find the square of a two digit whole number. Here's what I've discovered. For any two digit number, if you take the square of first digit, multiply the product of  digits by 2, take the square of the last digit and concatenate the numbers then you get the square of the two digit integer. Here's a couple of examples to clarify it:

Ex. 1) Find the square of 45.

Solution: 45²

                                     4                         5
                                     4²     2 x 4 x 5    5²
                                  =16    =40          =25
                                     1   10       2          5
                                     2025
Note: The matching colors are added together.

Therefore, square of 45=2025

This technique might not be theoretically provable. However, no matter what the number be between 10 and 99, it always gives the correct answer.

Ex. 2) Find the square of 99.
Solution: 99²

                                     9                         9
                                     9²     2 x 9 x 9    9²
                                  =81    =162         =81
                                    8  17           10       1
                                   9801

Therefore, square of 99=9801