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Check whether (l+m+n) is a factor of the...

Check whether (l+m+n) is a factor of the determinant `|{:(1+m,m+n,n+1),(" "n," "1," "m),(" "2," "2," "2):}|` or not. Give reason.

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`"Apply"R_1toR_1+R_2|{:(l+m+n,,m+n+l,,n+l+m),(n,,1,,m),(2,,2,,2):}|=2(l+m+n)|{:(1,,1,,1),(n,,1,,m),(1,,1,,1):}|`, "yes (l+m+n)is a factor".
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