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Let T:U ---> v be an isomorphism. Show that T^-1: V----> U is linear.

i. T^-1(0) = 0

ii. T^-1(-V) = -T^-1(V)

T^-1(-0) = T^-1(0+0)

= T^-1(0) + T^-1(0)

T^-1(0) = 0

T^-1(-V) = T^-1((-1)V)

=(-1)T^-1(V)

= -T^-1(V)

If T[x,y,z] = [x-y, y-z, x+z]

Then T is one-to-one right?

How do I show that T is onto?