## Matrix of the change of basis

Let $$A=((1{,}2,0{,}1)^T,(4{,}1,3{,}1)^T,(3{,}1,3{,}4)^T,(2{,}0,2{,}2)^T)$$,
$$B=((1{,}2,3{,}1)^T,(4{,}4,1{,}1)^T,(2{,}0,2{,}1)^T,(3{,}1,4{,}0)^T).$$
be two bases of $$\mathbb Z_5^4$$. Determine the matrices of the change of basis:

• #### Variant 1

$$[id]_{AK}$$, i.e. from the basis $$A$$ to the canonical basis.

• #### Variant 2

$$[id]_{KB}$$, i.e. from the canonical basis to the basis $$B$$.

• #### Variant 3

$$[id]_{AB}$$, i.e. from the basis $$A$$ to the basis $$B$$.