# what is the meaning of Det in the context of multiplication of two matrices

Does such a Determinant indicate a structural relationship between two variables for which matrices have been indicated.

• Do you mean this?
– M.B.
Nov 4 '13 at 15:08

Two by two matrices can be realised as linear transformations/functions on the plane. The determinant of a two by two matrix is the (signed) area of the transformation of the unit square (corners $(0,0),(1,0),(0,1),(1,1)$).
• Ah... well the first column of your matrix describes what the matrix will do to $(1,0)$ and the second column describes where $(0,1)$ will go. If the two columns are equal for example then the two points are sent to a single point and the transformed unit square is now a line... with an area of 0. Nov 4 '13 at 15:28