Zero Divisor of Ring/Examples/Order 2 Square Matrices/Example 2

Examples of Zero Divisors of Rings

Let $R$ be the ring square matrices of order $2$ over the real numbers.

Then:

$\begin {bmatrix} 0 & 1 \\ 0 & 0 \end {bmatrix} \begin {bmatrix} 1 & 0 \\ 0 & 0 \end {bmatrix} = \begin {bmatrix} 0 & 0 \\ 0 & 0 \end {bmatrix}$

demonstrating that $\begin {bmatrix} 0 & 1 \\ 0 & 0 \end {bmatrix}$ and $\begin {bmatrix} 1 & 0 \\ 0 & 0 \end {bmatrix}$ are zero divisors of $R$.

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): divisor of zero