In leson 27, we learned the efect of a transformation on a unit square by multiplying a matrix. for example,
a = 1
1 2
, 1
1 2

=
, 1
1 2

=
and 1
1 2

=
a. sasha says that we can multiply the inverse of a to those resultants of the square after the transformation to
get back to the unit square. is her conjecture corect? justify your answer.
b. from part (a), what would you say about the inverse matrix with regard to the geometric efect of
transformations?
c. a pure rotation matrix is
cos (theta) −sin (theta)
sin (theta) cos (theta) prove the inverse matrix for a pure rotation of

4
radians
counterclockwise is
cos − −sin −
− cos −
which is the same as

aa−b
−cc
aa−b
−b
aa−b

aa−b

d. prove that the inverse matrix of a pure dilation with a factor of 4 is
14
0
0 14
which is the same as


aa−b
−cc
aa−b
−b
aa−b

aa−b