Question

Show that if $F$ is a field, then $a 0=0$ for any $a$ in $F$. (Look at $a 0+a 0$.)

   Show that if $F$ is a field, then $a 0=0$ for any $a$ in $F$. (Look at $a 0+a 0$.)

Applied Algebra: Codes, Ciphers and Discrete Algorithms

Applied Algebra: Codes, Ciphers and Discrete Algorithms

Darel W. Hardy, Fred… 2nd Edition

Chapter 9, Problem 1

Instant Answer

Step 1

According to the distributive property of multiplication over addition in the field \(F\), we can factor out \(a\) from the expression. Thus, we have: \[ a \cdot 0 + a \cdot 0 = a \cdot (0 + 0) \] Show more…

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Show that if $F$ is a field, then $a 0=0$ for any $a$ in $F$. (Look at $a 0+a 0$.)

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