The digits 1 to 9 are arranged in three rows in such a way that each row contains three digits and t...........

Explanation:

We can only use three of the four digits – 2, 3, 7, and 9, in the first row.
The first digit in the first row cannot be 7 or 9, as otherwise thrice the number will not be a three-digit number.
So, the first digit in the first row can either be 2, or 3.
The possible cases are: 237, 273, 239, 293, 279, 297, 327, 372, 329, 392, 379, or 397.
On eliminating the numbers whose 3x is not a three-digit number, we are left with: 237, 273, 239, 293, 279, 297, 327, and 329.
We will check these numbers:
237 × 2 =474 (digit repetition, and so eliminated)
273 × 2 = 546; 273 × 3 = 819
239 × 2 = 478; 239 × 3 = 717 (digit repetition, and so eliminated)
293 × 2 = 586; 293 × 3 = 879 (digit repetition, and so eliminated)
279 × 2 = 558 (digit repetition, and so eliminated)
297 × 2 = 594 (digit repetition, and so eliminated)
327 × 2 = 654; 327 × 3 = 981
329× 2 = 658; 329× 3 = 987 (digit repetition, and so eliminated)
So, only two cases are possible.