Simple Linear algebra from Lienar Algebra and Retro Gamming
=> A (movement)
1 0 0
0 1 2
0 0 1
=> B (current position)
0 2 1
0 0 3
1 1 1
(0,0)(0,0) = 0
(0,1)(1,0) = 0
(0,2)(2,0) = 0
final result for index (0, 0) = 0
(1,0)(0,0) = 0
(1,1)(1,0) = 0
(1,2)(2,0) = 2
final result for index (1, 0) = 2
(2,0)(0,0) = 0
(2,1)(1,0) = 0
(2,2)(2,0) = 1 final result for index (2, 0) = 1
(0,0)(0,1) = 2
(0,1)(1,1) = 2
(0,2)(2,1) = 2
final result for index (0, 1) = 2
(1,0)(0,1) = 0
(1,1)(1,1) = 0
(1,2)(2,1) = 2
final result for index (1, 1) = 2
(2,0)(0,1) = 0
(2,1)(1,1) = 0
(2,2)(2,1) = 1
final result for index (2, 1) = 1
(0,0)(0,2) = 1
(0,1)(1,2) = 1
(0,2)(2,2) = 1
final result for index (0, 2) = 1
(1,0)(0,2) = 0
(1,1)(1,2) = 3
(1,2)(2,2) = 5
final result for index (1, 2) = 5
(2,0)(0,2) = 0
(2,1)(1,2) = 0
(2,2)(2,2) = 1
final result for index (2, 2) = 1
=> Result
0 2 1
2 2 5
1 1 1
=> F (rotation)
0 -1 0
0 0 0
0 0 1
=> G (current position)
0 2 1
0 0 3
1 1 1