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!

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- October 12th 2010, 05:24 PMsdh2106prove inverse transformation is linear
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! - October 12th 2010, 05:55 PMAlso sprach Zarathustra

Suppose linear transformation which is. Let us show now that is also linear transformation.__Bijection__

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. - October 14th 2010, 06:20 AMsdh2106
great explanation. thanks again!