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<b>let </b><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">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> 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="E1:93"/>
<font color="Maroon" title="c2">A</font> is <a href="matrixr2.html#V1" title="MATRIXR2:attr.1">invertible</a>
 ;<br/>

<a NAME="E2:93"/><b>then </b><i><font color="Green" title="E61">A2</font></i>: 
( <span class="p1">(<span class="default"><a href="matrixr2.html#K7" title="MATRIXR2:func.7">Inv</a> <font color="Maroon" title="c2">A</font></span>)</span> <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> <span class="p1">(<span class="default"><a href="matrixr2.html#K7" title="MATRIXR2:func.7">Inv</a> <font color="Maroon" title="c2">A</font></span>)</span> <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> )
 
<b>by </b><i><a class="ref" href="matrixr2.html#D6" target="_self" title="MATRIXR2:def.6">AA444</a></i>;<br/>
<a NAME="E3:93"/><b>then </b>
 <a href="matrixr2.html#K7" title="MATRIXR2:func.7">Inv</a> <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="ref" href="matrixr2.html#D5" target="_self" title="MATRIXR2:def.5">AA640</a></i>;<br/>
<b>hence </b><a NAME="E4:93"/>
 <a href="matrixr2.html#K7" title="MATRIXR2:func.7">Inv</a> <span class="p1">(<span class="default"><a href="matrixr2.html#K7" title="MATRIXR2:func.7">Inv</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font>
 <b>by </b><i><a class="txt" href="matrixr2.html#E2:93"><i><font color="Green" title="E61">A2</font></i></a>, <a class="ref" href="matrixr2.html#D6" target="_self" title="MATRIXR2:def.6">AA444</a></i>;<br/>


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