Could someone help me with the following problem?
Suppose A is a linear transformation from the x-y plane to itself. Show that A^-1 is also a linear transformation (if it exists).
Thanks for the help!
Suppose linear transformation which is Bijection. Let us show now that is also linear transformation.
Suppose , is a bijection, there are exist unique vectors which for them:
and .
From the linearity of we have also:
and .
Now, by definition of inverse transformation, , , and .
Hence:
and , therefor is linear transformation.