If D = $open vertical bar table row 1 1 1 row 1 cell 1 plus straight x end cell 1 row 1 1 cell 1 plus straight y end cell end table close vertical bar$ for x ≠ 0, y ≠ 0 then D is

divisible by neither x nor y

divisible by both x and y

divisible by x but not y

divisible by y but not x

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Solution

divisible by both x and y

straight D space equals space open vertical bar table row 1 1 1 row 1 cell 1 plus straight x end cell 1 row 1 1 cell 1 plus straight y end cell end table close vertical bar

C₂ → C₂ – C₁ & C₃ → C₃ – C₁

open vertical bar table row 1 0 0 row 1 straight x 0 row 1 0 straight y end table close vertical bar space equals space xy

Hence D is divisible by both x and y.

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