Description: Multiplying two transposed matrices results in the transposition of the product of the two matrices. (Contributed by Stefan O'Rear, 17-Jul-2018)
Ref | Expression | ||
---|---|---|---|
Hypotheses | mattposm.a | |
|
mattposm.b | |
||
mattposm.t | |
||
Assertion | mattposm | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mattposm.a | |
|
2 | mattposm.b | |
|
3 | mattposm.t | |
|
4 | eqid | |
|
5 | eqid | |
|
6 | simp1 | |
|
7 | 1 2 | matrcl | |
8 | 7 | simpld | |
9 | 8 | 3ad2ant3 | |
10 | 1 5 2 | matbas2i | |
11 | 10 | 3ad2ant2 | |
12 | 1 5 2 | matbas2i | |
13 | 12 | 3ad2ant3 | |
14 | 4 4 5 6 9 9 9 11 13 | mamutpos | |
15 | 1 4 | matmulr | |
16 | 9 6 15 | syl2anc | |
17 | 3 16 | eqtr4id | |
18 | 17 | oveqd | |
19 | 18 | tposeqd | |
20 | 17 | oveqd | |
21 | 14 19 20 | 3eqtr4d | |