Find transition matrices for [T]B1

[hank]

Given ordered bases B1={(1 0 0), (0,1,0), (0,0,1)}, B2 = {(1 1 2), (-1 -1 -1), (1 2 1)} and B3 = {(1 1 0), (1 3 1), (0 1 1)}
and A = [T]B2 = //B2 is a subscript
9 -4 2
16 -7 5
8 -4 5

Find transition matrices P12, P21, P13, P31, P23, and P32. //the numbers are subscripts
Then, use those to compute matrice B = [T]B1 and C=[T]B3.

Then, find minimum polynomial for A,B, and C.
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Ok, this homework is really long, but I just have a couple bullet point questions.

Question 1:
I found P12 = (B1)^-1 B2 = //product of the inverse of B1 and B2
-1 0 1
-3 1 1
-1 1 0

Is this correct? If not, what is the equation for finding P12?

Question 2:
I found B = [T]B1 = P21 * [T]B2 * P12 = //B1, 21, B2, 12 are all subscripts
1 -1 5
0 -1 0
-1 2 4

Is this correct? If not, what is the equation for finding [T]B1?

Question 3:
m(A) = (x-1)(x-3)

Is this correct?

Question 4:
Finally, what *exactly* am I finding? What is [T]B1? The professor is showing us all these examples, but he's not clearly stating what it's for.
I'm guessing [T]B1 is some sort of matrix used to transform a matrix of one Base into another.
What is the language for [T]B1? What is it called?

Thanks in advance,
--Hank