Given:
A/b - c = B/c - a = C/a - b

To find:
The value of Aa * Bb * Cc

Explanation:
We are given three expressions that are equal to each other:

A/b - c = B/c - a = C/a - b

To solve this, we can use the method of cross-multiplication. Let's start by setting up equations for each pair of expressions:

A/b - c = B/c - a
=> A/b - B/c = c - a

B/c - a = C/a - b
=> B/c - C/a = a - b

C/a - b = A/b - c
=> C/a - A/b = b - c

Now, let's cross-multiply the first pair of equations:

A/c - B/b = cb - ab

Similarly, cross-multiplying the other two pairs of equations:

B/a - C/c = ac - bc
C/b - A/a = ba - ca

Now, let's add all three cross-multiplication equations:

(A/c - B/b) + (B/a - C/c) + (C/b - A/a) = (cb - ab) + (ac - bc) + (ba - ca)

Simplifying the equation:

A/c - C/c + B/a - A/a + C/b - B/b = cb - ab + ac - bc + ba - ca

Combining like terms:

(A - C)/c + (B - A)/a + (C - B)/b = cb - ab + ac - bc + ba - ca

Now, we notice that the left side of the equation is equal to 0, since we have the same terms in the numerator and denominator. Therefore, the equation simplifies to:

0 = cb - ab + ac - bc + ba - ca

Rearranging the terms:

0 = ab - ba + bc - cb + ca - ac

Simplifying further:

0 = 0

Since the equation is always true, regardless of the values of a, b, and c, we can conclude that the value of Aa * Bb * Cc is 0 (option IV).

Answer:
The value of Aa * Bb * Cc is 0.