Consider the following statements: Statement-I: If X is an n × n...

Statement-I states that for an $n \times n$ matrix $X$, $\det(mX) = m^n \det(X)$. 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 $n$ times (once for each row), we can factor out $m$ from each of the $n$ rows, yielding $m^n \det(X)$.

Thus, Statement-II provides the logical reasoning required to prove Statement-I. Both statements are correct, and Statement-II explains Statement-I.