Solution of aXb equals c and bxc equals a?

Answer 1

The only way this could be true is under one of the following conditions:

• a, b and c are all equal to zero
• b is equal to 1 and a is equal to c
• b is equal to -1 and a is equal to -c

Consider:

ab = c

bc = a

First, plug the second equation into the first one to find the value of b:

(bc)(b) = c

b2c = c

b2 = 1

b = ±1

Now take those values and plug it into either equation:

(1)(c) = a

c = a

or:

(-1)(c) = a

c = -a

To prove that the absolute values of c and a must be identical:

Given:

ab = c

bc = a

Then:

ab/c = 1

bc/a = 1

Therefore:

ab/c = bc/a

a2b = bc2

a2 = c2

|a| = |c|