Olympiad matrix question

[kind wing]

well what have you tried

if the inverse only contains integers then what does it imply about the determinant

[simple dragon]

we can say m=!kn since if m=kn then |A|=0 and try some first values for n

u can see u can subract row 1 row 2 and u get 0 k-m 0 0 … 0 so we can reduce the matrix

[simple dragon]

u get |A|=(m-k)^n-1

[minor cairn]

This seems very solved ...