Zero Divisor of Ring/Examples/Order 2 Square Matrices/Example 4
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Examples of Zero Divisors of Rings
Let $R$ be the ring of square matrices of order $2$ over the real numbers.
Then:
- $\begin {bmatrix} 1 & 1 \\ 1 & 1 \end {bmatrix} \begin {bmatrix} -1 & 1 \\ 1 & -1 \end {bmatrix} = \begin {bmatrix} 0 & 0 \\ 0 & 0 \end {bmatrix}$
demonstrating that $\begin {bmatrix} 1 & 1 \\ 1 & 1 \end {bmatrix}$ and $\begin {bmatrix} -1 & 1 \\ 1 & -1 \end {bmatrix}$ are zero divisors of $R$.
Sources
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): zero divisor