Based on complex arithmetic for MX=B, for

| 1 + i , 2+i |
|.................| = A
| 1 -2i , 2-i |

| 3 + i |
|.........| = X
| 2 + i |

then
| 5 + 8i |
|...........| = B and determinant of A = -1 + 4j
| 10 - 5i |

However, when I try to calculate the determinant and / or the inverse of A in the code below to solve for X, the results are not at all what are to be expected. Please can you identify what I'm missing. Thanks.

#! /usr/bin/perl -w
use strict;    
use CGI::Carp qw(warningsToBrowser fatalsToBrowser); 
use CGI qw(:standard escapeHTML);    
use PDL;
use PDL::Complex;

my $matrixM = pdl [ [ 1+1*i, 2+1*i],[ 1-2*i, 2-1*i] ];
my $matrixB = pdl [ 5+8*i, 10-5*i ];
my $matrixX = pdl [ ];

print header (), start_html (-title => "Matrix Ops");
print "<H1><center>Via Perl Data Language</center></H1><br>\n";


print "\$matrixM = ", $matrixM,"<br>\n";
print "determinant of \$matrixM = ",$matrixM->det,"<br>\n";
print "inverse of \$matrixM = ",$matrixM->det,"<br>\n";
print "\$matrixB = ", $matrixB,"<br>\n";
print "\$matrixX = ", $matrixM->inv x $matrixB,"<br>\n";

print end_html ();
exit(0);
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