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?

Step-by-step solution

Statement-I states that for an n n matrix X , (mX) = m^n (X) . This is a standard property of determinants and is correct. Statement-II states that if a single row or column of a matrix is multiplied by a scalar m , the determinant of the resulting matrix is m times the determinant of the original matrix. This is also a fundamental property of determinants and is correct. Multiplying a matrix X by a scalar m is equivalent to multiplying each of its n rows by m . By applying the property given in Statement-II n time