$\Rightarrow \mathrm{Q}_{\mathrm{ABCA}}=\mathrm{W}_{\mathrm{ABCA}}$

$\Rightarrow \mathrm{Q}_{\mathrm{A} \rightarrow \mathrm{B}}+\mathrm{Q}_{\mathrm{B} \rightarrow \mathrm{C}}+\mathrm{Q}_{\mathrm{C} \rightarrow \mathrm{A}}$

$=\mathrm{W}_{\mathrm{A} \rightarrow \mathrm{B}}+\mathrm{W}_{\mathrm{B} \rightarrow \mathrm{C}}+\mathrm{W}_{\mathrm{C} \rightarrow \mathrm{A}}$   $.(1)$

Given $Q_{B \rightarrow C}+Q_{C \rightarrow A}=W_{A \rightarrow B}+W_{B \rightarrow C}$  $(2)$

Subtracting $( 2)$ from $( 1)$

$\mathrm{Q}_{\mathrm{A} \rightarrow \mathrm{B}}=\mathrm{W}_{\mathrm{C} \rightarrow \mathrm{A}}=0$

(as process $\mathrm{C} \rightarrow \mathrm{A}$ is isochoric)

process $A \rightarrow B$ is adiabatic.