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<b>let </b><font color="Maroon">n</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">K</font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">M1</font> be   <a href="matrix_1.html#NM5">Matrix</a> of <font color="Maroon">n</font>,<font color="Maroon">K</font>;<br/>





<b>assume </b><a NAME="E1:32"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">M1</font> is <a href="matrix_8.html#V4" target="_self">Self_Reversible</a>
 ;<br/>

<a NAME="E2:32"/><b>then </b>
( <font color="Maroon">M1</font> is <a href="matrix_6.html#V1">invertible</a> &amp; <font color="Maroon">M1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">M1</font> <a href="matrix_6.html#K5">~</a>  )
 
<b>by </b><i/>;<br/>
<a NAME="E3:32"/><b>then </b>
<font color="Maroon">M1</font> <a href="matrix_6.html#K5">~</a>  <a href="matrix_6.html#R2">is_reverse_of</a> <font color="Maroon">M1</font>
 
<b>by </b><i><a class="ref" href="matrix_6.html#D4">MATRIX_6:def 4</a></i>;<br/>
<a NAME="E4:32"/><b>then </b><i><font color="Green">E37</font></i>: 
<font color="Maroon">M1</font> <a href="matrix_6.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">M1</font> <a href="matrix_6.html#K5">~</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K12">1.</a> <font color="Maroon">K</font>,<font color="Maroon">n</font>
 
<b>by </b><i><a class="ref" href="matrix_6.html#D2">MATRIX_6:def 2</a></i>;<br/>
<a NAME="E5:32"/>
<font color="Maroon">M1</font> <a href="matrix_6.html#K4">*</a> <font color="Maroon">M1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">M1</font> <a href="matrix_6.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">M1</font> <a href="matrix_6.html#K5">~</a> </span>)</span>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:32"/>
<font color="Maroon">M1</font> is <a href="matrix_8.html#V3" target="_self">Involutory</a>
 <b>by </b><i>, </i>;<br/>


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