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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E60">Th51</font></span>: <a NAME="T51"><span class="comment"><font color="firebrick">:: MATRIX11:51</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">K</font> being   <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b3">A</font> being   <a href="matrix_1.html#NM2" title="MATRIX_1:NM.2">Matrix</a> of <font color="Olive" title="b1">n</font>,<font color="Olive" title="b2">K</font>  st  not <font color="Olive" title="b2">K</font> is  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>  &amp; <font color="Olive" title="b2">K</font> is  <a href="vectsp_1.html#V4" title="VECTSP_1:attr.4">well-unital</a>  &amp; <font color="Olive" title="b2">K</font> is  <a href="vectsp_2.html#V1" title="VECTSP_2:attr.1">domRing-like</a>  holds <br/> for <font color="Olive" title="b4">i</font>, <font color="Olive" title="b5">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b4">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Olive" title="b1">n</font> &amp; <font color="Olive" title="b5">j</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Olive" title="b1">n</font> &amp; <font color="Olive" title="b4">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">j</font> holds <br/> <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><a href="matrix11.html#NK5" title="MATRIX11:NK.5">RLine</a> (<font color="Olive" title="b3">A</font>,<font color="Olive" title="b4">i</font>,<span class="p2">(<span class="default"><a href="matrix_0.html#K7" title="MATRIX_0:func.7">Line</a> (<font color="Olive" title="b3">A</font>,<font color="Olive" title="b5">j</font>)</span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b2">K</font></div></div>
