Linear algebra, computing n-order determinant DN = [a, a a x][a a… xa]… [a x… a a][x a… a a]

Linear algebra, computing n-order determinant DN = [a, a a x][a a… xa]… [a x… a a][x a… a a]

Add columns 2, 3, n to column 1,
Then subtract line n from lines 1, 2,..., n-1,
D = (- 1) ^ [n (n-1) / 2] [x + (n-1) a] (x-a) ^ (n-1)

A brief answer to the calculation of n-order determinant of linear algebra
1 2 2 ···2
2 2 2···2
2 2 3···2
··· ·
··· ·
2 2 2···N
1 2 2···2
2 2 2···2
D= 2 2 3···2
·····There are two vertical lines on the left and right. An ellipsis means all the way to n
··· · ·
2 2 2···N

Subtract line 1 from line 2-N to get line 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

How to calculate the determinant of linear algebra?
1 0 0 x
x 1 0 0
0 x 1 0
0 0 x 1
How to calculate this determinant?