I haven't looked at Strang's approach.

The "x = b / A" is a bit of a gut-punch on first look because my mind immediately tells me all the ways that that does not work. It makes a some sense once I take a second to think about it, and I can see why it would make you want to jump in a little deeper, but matrices being non-commutative makes me cringe at the idea of a division operator which does not very very clearly spell out where it appears in the chain.

Ax = b is all well and good, but AxA^-1 = bA^-1 is not meaningful; the application/composition order is very important.