If [x 1 1] [1 2 3; 4 5 6; 7 8 9] [1; 1; x] = [45], then which one of the following is a value of x?

First compute [1 2 3; 4 5 6; 7 8 9][1; 1; x] = [1+2+3x; 4+5+6x; 7+8+9x] = [3+3x; 9+6x; 15+9x]. Then [x 1 1]·[3+3x; 9+6x; 15+9x] = x(3+3x) + (9+6x) + (15+9x) = 3x + 3x² + 9 + 6x + 15 + 9x = 3x² + 18x + 24 = 45. So 3x² + 18x - 21 = 0, x² + 6x - 7 = 0, (x+7)(x-1) = 0, giving x = 1 or x = -7. Among options, x = 1 is correct.