Show that a-b-a-c- may not imply that b-c-

( a × b #160; ) = a × c #160; ⇒ a × b a × c =0 ⇒ a × b + c × a =0 ⇒ a ×( b + c #160; ) =0 ⇒ a =0 ⇒ b + c =0 ...

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Question

Show that $\to a \times \to b = \to a \times \to c$ may not imply that $\to b = \to c$ .

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\to a + \to b + \to c = \to 0

\to a \times \to b = \to b \times \to c = \to c \times \to a

\to a, \to b, \to c

\to a, \to b, \to c

\to a \times \to b = \to b \times \to c = \to c \times \to a

[\to a \to b \to c] = 0.

\to a, \to b, \to c

\to a \times \to b = \to c, \to b \times \to c = \to a, \to c \times \to a = \to b

| \to a | = | \to b | = | \to c |

\to a, \to b, \to c

\to a . \to b = \to a . \to c, \to a \times \to b = \to a \times \to c, \to a \neq 0

\to b = \to c

\to a, \to b, \to c

\to a + \to b + \to c = \to 0,

\to a \times \to b = \to b \times \to c = \to c \times \to a,

[\to a \to b \to c] = 0.

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