Determinant_with_Row_Multiplied_by_Constant

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.