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<b>let </b><font color="Maroon" title="c1">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>let </b><font color="Maroon" title="c2">K</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>;<br/><b>let </b><font color="Maroon" title="c3">M2</font>, <font color="Maroon" title="c4">M1</font> be   <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">K</font>;<br/>







<b>assume </b><a NAME="E1:45"/><i><font color="Green" title="E10">A1</font></i>: 
( <font color="Maroon" title="c3">M2</font> is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> &amp; <font color="Maroon" title="c4">M1</font> <a href="matrix_8.html#R1" title="MATRIX_8:pred.1">is_similar_to</a> <font color="Maroon" title="c3">M2</font> )
 ;<br/>

<b>then consider </b><font color="Maroon" title="c5">M4</font> being   <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">K</font><b> such that </b><br/><a NAME="E3:45"/><i><font color="Green" title="E11">A2</font></i>: 
( <font color="Maroon" title="c5">M4</font> is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> &amp; <font color="Maroon" title="c4">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">M4</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c3">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c5">M4</font> )
 <b>by </b><i><a class="ref" href="matrix_8.html#D5" target="_self" title="MATRIX_8:def.5">Def5</a></i>;<br/>
<a NAME="E4:45"/>
( <font color="Maroon" title="c5">M4</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a>  is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c5">M4</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">M4</font> )
 
<b>by </b><i><a class="txt" href="matrix_8.html#E3:45"><i><font color="Green" title="E11">A2</font></i></a>, <a class="ref" href="matrix_6.html#T16" title="MATRIX_6:th.16">MATRIX_6:16</a></i>;<br/>
<a NAME="E5:45"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">M4</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c3">M2</font> is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>
 
<b>by </b><i><a class="txt" href="matrix_8.html#E1:45"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="matrix_6.html#T37" title="MATRIX_6:th.37">MATRIX_6:37</a></i>;<br/>
<b>hence </b><a NAME="E6:45"/>
<font color="Maroon" title="c4">M1</font> is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>
 <b>by </b><i><a class="txt" href="matrix_8.html#E3:45"><i><font color="Green" title="E11">A2</font></i></a>, <a class="ref" href="matrix_6.html#T37" title="MATRIX_6:th.37">MATRIX_6:37</a></i>;<br/>


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