The following comes from Shakuntala Devi's book
"Figuring - The Joy of Numbers" page 123 :
Multiplying the number 12345679 by the multiples of 9,
gives a curious set of palindromic patterns :

12345679 x 9 = 111111111
12345679 x 18 = 222222222
12345679 x 27 = 333333333
and so on.

Multiplying by 999999999 itself gives a number which is a mirror image of itself
12345679 x 999999999 = 12345678987654321
incidentally, this product is a perfect square [ It's also Palindromic Square nr. 91 ]

111111111 ² = 12345678987654321

Many people find the above square quite useless but nevertheless fascinating !