Show that matrix $(ABC)^T = C^T B^T A^T$

Question

Relevant theorem: $(AB)^T = B^T A^T$

Clearly it looks similar to what we want, but not sure how invoke it. Maybe with associativity?

Answer 1

$(ABC)^T = ((AB)C)^T = C^T (AB)^T = C^T B^T A^T$

Answer 2

$(ABC)^{T}=((AB)C)^{T}=C^{T}(AB)^{T}=C^{T}B^{T}A^{T}$.

Answer 3

Just apply the rule:

$$(ABC)^t=((AB)C)^t=(DC)^t=C^tD^t=C^t(AB)^t=.....$$

Where $D=AB$