Determinant with Row Multiplied by Constant

Theorem
Let $\mathbf A = \sqbrk a_n$ be a square matrix of order $n$.

Let $\map \det {\mathbf A}$ be the determinant of $\mathbf A$.

Let $\mathbf B$ be the matrix resulting from one row of $\mathbf A$ having been multiplied by a constant $c$.

Then:
 * $\map \det {\mathbf B} = c \map \det {\mathbf A}$

That is, multiplying one row of a square matrix by a constant multiplies its determinant by that constant.

Also see

 * Determinant with Column Multiplied by Constant