Matrices Modulo m

To reduce a matrix A modulo m, enter the expression A$\limfunc$modm and evaluate it.


$\blacktriangleright$ Evaluate

$\left[\vphantom{ \begin{array}{cc} 5 & 8 \\ 9 & 4 \end{array} }\right.$$\begin{array}{cc} 5 & 8 \\ 9 & 4 \end{array}$$\left.\vphantom{ \begin{array}{cc} 5 & 8 \\ 9 & 4 \end{array} }\right]$$\limfunc$mod3 = $\left[\vphantom{ \begin{array}{cc} 2 & 2 \\ 0 & 1 \end{array} }\right.$$\begin{array}{cc} 2 & 2 \\ 0 & 1 \end{array}$$\left.\vphantom{ \begin{array}{cc} 2 & 2 \\ 0 & 1 \end{array} }\right]$

$\left(\vphantom{ \begin{array}{ccc} 3 & 7 & 5 \\ 5 & 4 & 8 \\ 2 & 0 & 5 \end{array} }\right.$$\begin{array}{ccc} 3 & 7 & 5 \\ 5 & 4 & 8 \\ 2 & 0 & 5 \end{array}$$\left.\vphantom{ \begin{array}{ccc} 3 & 7 & 5 \\ 5 & 4 & 8 \\ 2 & 0 & 5 \end{array} }\right)^{{-1}}_{}$$\limfunc$mod11 = $\left(\vphantom{ \begin{array}{ccc} 9 & 9 & 3 \\ 2 & 5 & 1 \\ 3 & 3 & 10 \end{array} }\right.$$\begin{array}{ccc} 9 & 9 & 3 \\ 2 & 5 & 1 \\ 3 & 3 & 10 \end{array}$$\left.\vphantom{ \begin{array}{ccc} 9 & 9 & 3 \\ 2 & 5 & 1 \\ 3 & 3 & 10 \end{array} }\right)$

$\left(\vphantom{ \begin{array}{ccc} 3 & 7 & 5 \\ 5 & 4 & 8 \\ 2 & 0 & 5 \end{array} }\right.$$\begin{array}{ccc} 3 & 7 & 5 \\ 5 & 4 & 8 \\ 2 & 0 & 5 \end{array}$$\left.\vphantom{ \begin{array}{ccc} 3 & 7 & 5 \\ 5 & 4 & 8 \\ 2 & 0 & 5 \end{array} }\right)$ $\left(\vphantom{ \begin{array}{ccc} 9 & 9 & 3 \\ 2 & 5 & 1 \\ 3 & 3 & 10 \end{array} }\right.$$\begin{array}{ccc} 9 & 9 & 3 \\ 2 & 5 & 1 \\ 3 & 3 & 10 \end{array}$$\left.\vphantom{ \begin{array}{ccc} 9 & 9 & 3 \\ 2 & 5 & 1 \\ 3 & 3 & 10 \end{array} }\right)$$\limfunc$mod11 = $\left(\vphantom{ \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} }\right.$$\begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}$$\left.\vphantom{ \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} }\right)$



\begin{example} The \index{Hamming code@Hamming code}Hamming (7,4) code oper... ... 1 \\ 1 & 1 & 0 \\ 1 & 1 & 1 \end{array} \right] \bigskip $ \end{example}


\begin{example} The matrix product $\mathbf{c}P\limfunc{mod}2=\left[ \begin{a... ...gin{array}{cccc} 1 & 0 & 1 & 1 \end{array} \right] $.\bigskip \end{example}


\begin{example} A \textsl{two-by-two } \index{Block cipher@Block cipher}\text... ... 2 \end{array} \right] . \end{displaymath} \bigskip\medskip \end{example}