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<b>let </b><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">B1</font>, <font color="Maroon" title="c4">B2</font> be   <a href="matrix_1.html#NM3" title="MATRIX_1:NM.3">Matrix</a> of <font color="Maroon" title="c1">n</font>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>



<b>assume </b><a NAME="E1:89"/><i><font color="Green" title="E61">A1</font></i>: 
( <font color="Maroon" title="c3">B1</font> <a href="matrixr2.html#K1" title="MATRIXR2:func.1">*</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixr2.html#K4" title="MATRIXR2:func.4">1_Rmatrix</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c2">A</font> <a href="matrixr2.html#K1" title="MATRIXR2:func.1">*</a> <font color="Maroon" title="c4">B2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixr2.html#K4" title="MATRIXR2:func.4">1_Rmatrix</a> <font color="Maroon" title="c1">n</font> )
 ;<br/>

<a NAME="E2:89"/><b>then </b><i><font color="Green" title="E62">A2</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">B1</font> <a href="matrixr2.html#K1" title="MATRIXR2:func.1">*</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="matrixr2.html#K1" title="MATRIXR2:func.1">*</a> <font color="Maroon" title="c4">B2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B2</font>
 
<b>by </b><i><a class="ref" href="matrixr2.html#T70" target="_self" title="MATRIXR2:th.70">Th70</a></i>;<br/>
<i><font color="Green" title="E63">A3</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c3">B1</font> <a href="matrixr2.html#K1" title="MATRIXR2:func.1">*</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="matrixr2.html#K1" title="MATRIXR2:func.1">*</a> <font color="Maroon" title="c4">B2</font> = 
<font color="Maroon" title="c3">B1</font> <a href="matrixr2.html#K1" title="MATRIXR2:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="matrixr2.html#K1" title="MATRIXR2:func.1">*</a> <font color="Maroon" title="c4">B2</font></span>)</span>
<b>by </b><i><a class="ref" href="matrixr2.html#T28" target="_self" title="MATRIXR2:th.28">Th28</a></i>
<br/>.= 
<font color="Maroon" title="c3">B1</font>
<b>by </b><i><a class="txt" href="matrixr2.html#E1:89"><i><font color="Green" title="E61">A1</font></i></a>, <a class="ref" href="matrixr2.html#T71" target="_self" title="MATRIXR2:th.71">Th71</a></i>
;<br/>
<b>hence </b><a NAME="E4:89"/>
<font color="Maroon" title="c3">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B2</font>
 <b>by </b><i><a class="txt" href="matrixr2.html#E1:89"><i><font color="Green" title="E61">A1</font></i></a>, <a class="ref" href="matrixr2.html#T70" target="_self" title="MATRIXR2:th.70">Th70</a></i>;<br/>

<b>thus </b><a NAME="E5:89"/>
<font color="Maroon" title="c2">A</font> is <a href="matrixr2.html#V1" title="MATRIXR2:attr.1">invertible</a>
 <b>by </b><i><a class="txt" href="matrixr2.html#E1:89"><i><font color="Green" title="E61">A1</font></i></a>, <a class="txt" href="matrixr2.html#E2:89"><i><font color="Green" title="E62">A2</font></i></a>, <a class="txt" href="matrixr2.html#E3:89"><i><font color="Green" title="E63">A3</font></i></a>, <a class="ref" href="matrixr2.html#D5" target="_self" title="MATRIXR2:def.5">Def5</a></i>;<br/>


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