In a third order determinant,each element of | vedclass

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(D) The property of determinants states that if each element of a column (or row) is the sum of $k$ terms,the determinant can be expressed as the sum

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$24$

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(D) The property of determinants states that if each element of a column (or row) is the sum of $k$ terms,the determinant can be expressed as the sum of $k$ determinants.Given a $3 	imes 3$ determinant:Column $1$ has $2$ terms,so it can be split into $2$ determinants.Column $2$ has $3$ terms,so each of those $2$ determinants can be split into $3$ determinants,resulting in $2 	imes 3 = 6$ determinants.Column $3$ has $4$ terms,so each of those $6$ determinants can be split into $4$ determinants,resulting in $6 	imes 4 = 24$ determinants.Therefore,the total number of determinants $n = 2 	imes 3 	imes 4 = 24$.

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