Question

In a third order determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms. Then, it can be decomposed into $n$ determinants, when $n$ has the value

• A. $1$
• B. $9$
• C. $16$
• D. $24$

Answer 1

The correct option is D $24$

Column one can be divided into 2 determinants .

In each of those two determinants, column 2 can be divided into 3 different determinants, thus making a total of 6. And each of those 6 determinants can be divided into 4 determinants, by seperating out 3rd column.

Hence, total determinants thus formed $=2\times 3\times 4=24$