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Properties of Determinants

If each eleme...

Question

If each element in a row of a determinant is multiplied by the same factor $r$ , then the value of the determinant :

A

Is multiplied by

r^{3}

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B

Is increased by

3 r

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C

Remains unchanged

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D

Is multiplied by

r

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Solution

The correct option is D Is multiplied by $r$
If one of the row is multiplied by $r$ , then while finding the determinant we can take $r$ common from the determinant.
So, the determinant will be $r$ times the value of determinant without multiplying $r$ to each element of a row.
Hence, option D is correct.

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