Model Matrix Interacting model

Question

[akh22]

I am using edgeR's glm approach to determine dge of two groups, wide type (WT) and transgenic (TR) mice, both of which receive four sets of treatment, A, B, A+B, and saline) as follows,

    mouse treatment
1:    TR       A+B
2:    TR         A
3:    TR         B
4:    TR    Saline
5:    WT       A+B
6:    WT         A
7:    WT         B
8:    WT    Saline

I have a design. matrix like this;

         TR-A+B  TR-A  TR-B     TR-saline  WT-A+B  WT-A   WT-B   WT-Saline
1           1      0      0         0          0      0      0         0
2           1      0      0         0          0      0      0         0
3           0      1      0         0          0      0      0         0
4           0      1      0         0          0      0      0         0
5           0      0      1         0          0      0      0         0
6           0      0      1         0          0      0      0         0
7           0      0      0         1          0      0      0         0
8           0      0      0         1          0      0      0         0
9           1      0      0         0          1      0      0         0
10          0      0      0         0          1      0      0         0
11          0      0      0         0          0      1      0         0
12          0      0      0         0          0      1      0         0
13          0      0      0         0          0      0      1         0
14          0      0      0         0          0      1      1         0
15          0      0      0         0          0      0      0         1
16          0      0      0         0          0      0      0         1

To determine dge of TR vs WT truly due to combo A+B treatment, should a following contrast be used

(TR-A+B - TR-A - TR-B - TR-saline)-(WT-A+B - WT-A - WT-B - WT-Saline ) ?

Or can I use this by creating an new interactive matrix ,

model, matrix( ~ treatment*mouse, data=d)

(Intercept), mouseWT, treatmentA+B, treatmentB, treatmentSaline, mouseWT:treatmentA+B `           

mouseWT:treatmentB mouseWT:treatmentSaline`

and do `glmQLFTest ?

Thanks.