Consider the following statements : Statement-I : If X is an n n matrix, then (mX)=m^n (X), where m is a scalar. Statement-II : If Y is a matrix obtained from X by multiplying any row or column by a scalar m, then (Y)=m (X). Which one of the following is correct in respect of the above statements?

NDA 2025 Mathematics question

Consider the following statements : Statement-I : If is an matrix, then , where is a scalar. Statement-II : If is a matrix obtained from by multiplying any row or column by a scalar , then . Which one of the following is correct in respect of the above statements?

(A)Both Statement-I and Statement-II are correct and Statement-II explains Statement-ICorrect
(B)Both Statement-I and Statement-II are correct but Statement-II does not explain Statement-I
(C)Statement-I is correct but Statement-II is not correct
(D)Statement-I is not correct but Statement-II is correct

Answer: (A)

Solution

Statement-II is a standard property: multiplying one row (or column) of a matrix by multiplies its determinant by . The matrix is obtained from by multiplying

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Question ID VK-030175