# Linear Algebra: Determinant

by drosales
Tags: algebra, determinant, linear
 P: 9 I need help with another homework problem Let n be a positive integer and An*n a matrix such that det(A+B)=det(B) for all Bn*n. Show that A=0 Hint: prove property continues to hold if A is modified by any finite number of row or column elementary operations It seems obvious that A=0 but i'm having trouble developing the proof. Any help would be great.
 Mentor P: 15,957 Please post homework in the homework forum. I moved it for you now. A hint for the proof: can you write a row/column operation as an elementary matrix??
 P: 9 Yes and the product of the elementary matrices returns A=E1*E2*..*En is this what you are referring to?
Mentor
P: 15,957

## Linear Algebra: Determinant

Yes. Let E be an elementary matrix, can you show that

$$det(EA+B)=det(B)$$

??
 P: 9 Im not quite sure how to show this
 Mentor P: 15,957 Hint: $B=EE^{-1}B$. Use that $det(XY)=det(X)det(Y)$.

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