+0  
 
-3
65
3
avatar+115 

Hey guys! I need help this this question:

 

Given that \(\begin{vmatrix} a & b & c \\ d & e & f \\ g & h & i \end{vmatrix} = -24\), find \(\begin{vmatrix} a & d & g \\ b & e & h \\ c & f & i \end{vmatrix}\). I tried constructing a matrix with a determinant of 24 but couldn't find one. Does anyone have ideas?

 May 30, 2020
 #1
avatar+30686 
+2

Look very carefully at the terms on the right-hand side of equations (1) and (2) below.  What do you notice?

 

 May 30, 2020
 #3
avatar+115 
0

Oh! That's a really cool. So does that mean if you rotate a matrix, its determinant stays the same?

somebody  May 30, 2020

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