What Happens to $\det(A)$ If We Perform an Elementary Row Operation on $A$
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Mathematics/Linear Algebra
What Happens to $\det(A)$ if we perform an elementary row operation on $A$Theorem 1. Let $A \in M_{n \times n}(F)$ and $B = R(A)$, where $R$ is an elementary row operation. Then the followings hold:(a) If $R = R_{i \leftrightarrow j}$, then $\det(B) = -\det(A)$.(b) If $R = R_{ci}$, then $\det(B) = c \cdot \det(A)$.(c) If $R = R_{i + cj}$, then $\det(B) = \det(A)$.