(A) In Boolean algebra,the variable $A$ can only take two values: $0$ or $1$.If $A = 0$,then $\bar{A} = 1$. Therefore,$A \cdot \bar{A} = 0 \cdot 1 = 0

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(A) In Boolean algebra,the variable $A$ can only take two values: $0$ or $1$.If $A = 0$,then $\bar{A} = 1$. Therefore,$A \cdot \bar{A} = 0 \cdot 1 = 0$.If $A = 1$,then $\bar{A} = 0$. Therefore,$A \cdot \bar{A} = 1 \cdot 0 = 0$.In both possible cases,the result is $0$. Thus,$A \cdot \bar{A} = 0$.