Upcoming midterms are giving me very little time to work on assignments such as this one, so I need help with this.

Suppose

is a vector space over a field

.

Suppose

is a basis for

,

is a linear operator with matrix

with respect to

,

is a linear operator with matrix

with respect to

.

**a)** Prove that the composition

is a linear. (typo?)

**b)** Prove that the matrix of

with respect to

is

by proving that the

th entry of the matrix of

is

.

A hint provided is as follows: Expand

then use this expansion to expand

.

This is probably quite easy, but as I said before, I can't devote too much time to this or I'll not be able to properly prepare for my midterms.