111,111,111 x 111,111,111 = 12345678987654321
145 = 1! + 4! + 5!
90 ==> 9 + 0 = 9, 81 ==> 8 + 1 = 9, 72 ==> 7 + 2 = 9, etc.
Zero does not equal zero: 0+0+0+0... equals (-1+1)+(-1+1)+(-1+1)..., which (using the associative property of addition) equals -1+(1+-1)+(1+-1)+(1+-1)..., which equals -1.
The sum of each column equals each other!
987654321
123456789
87654321
123456780
7654321
123456700
654321
123456000
54321
123450000
4321
123400000
321
123000000
21
120000000
+ 1
+ 100000000