i've been told ABxAC is defined as:

| i j k |
| ab1 ab2 ab3 |
| ac1 ac2 ac3 |

ie,

i([ab2][ac3] - [ac2][ab3]) - j([ab1][ac3] - [ac1][ab3]) + k([ab1][ac2] - [ac1][ab2])

and that (ABxAC).AD is defined as

letting [ab2][ac3] - [ac2][ab3] = x
letting -([ab1][ac3] - [ac1][ab3]) = y
letting [ab1][ac2] - [ac1][ab2] = z

can the whole (ABxAC).AD just be simplified to...

| ab1 ab2 ab3 |
| ac1 ac2 ac3 |

it just seems a neater way of doing it to me...
A = (a1,a2,a3)
B = (b1,b2,b3)
C = (c1,c2,c3)

In general, A.(BxC) is the determinent of the matrix who's rows are A, B, C.

ie determinent of the the matrix

a1 a2 a3
b1 b2 b3
c1 c2 c3

Galois.
Galois
A = (a1,a2,a3)
B = (b1,b2,b3)
C = (c1,c2,c3)

In general, A.(BxC) is the determinent of the matrix who's rows are A, B, C.

ie determinent of the the matrix

a1 a2 a3
b1 b2 b3
c1 c2 c3

Galois.

the only method we were shown involves working out bxc first and then dotting it with a. but mark schemes say 'or equivalent method' and i noticed dotting a with bxc seemed to be just finding the 3x3 determinant of abc and was wonderining if this was a recognised method of working out a.(bxc) or was a mathematical fluke of some sort...
El Stevo
the only method we were shown involves working out bxc first and then dotting it with a. but mark schemes say 'or equivalent method' and i noticed dotting a with bxc seemed to be just finding the 3x3 determinant of abc and was wonderining if this was a recognised method of working out a.(bxc) or was a mathematical fluke of some sort...

No fluke, definaltey recognised. It comes from the definition.

It's like saying what's 5 times ( 4 + 98 + 36 + 3).

One could naively. multiply 5 through each term in the bracket, whereas another would add the sum in the bracket first and carry out just one multiplication.

Galois.