Let the three digit numbers A28,3B9,62C where A, B, C are integers between 0 and 9 , be divisible by a fixed integer k. Show that the determinant A 3689C 2 B 2is divisible by k

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Please find the answer to your question below
AsA28,3B9,62C where A, B, C are integers between 0 and 9 , be divisible by a fixed integer k then there exist m1,m2,m3 such that
100A+20+8=km1
300+10B+9=km2
600+20+c=km3
Applying R2=R2+100R1+10R2 we get

Whereis an integer
Since A,m1,m2,m3,B are integers
Thusis divisible by k