The code would be shorter, and would most likely be easier to read and maintain (and extend), if you used an AoA for the matrix Entry widgets and another AoA (with a slightly different name) to hold the Entry widget values; these two tightly-related data structures could be configured in a loop (the following is not tested, but should be close to usable):

my $last_row = 2;
my $last_col = 2;
my $matrix_entry;
my $matrix_value;

for my $row (0 .. $last_row) {
  my $row_frame = $MW->Frame()->pack(-expand => '1',
                                     -fill => 'none',
                                     -side => 'top');
  for my $col (0 .. $last_col) {
    $$matrix_entry[$row][$col] = 
       $row_frame->Entry(-font => 'bold',
                         -width => '3',
                         -relief => 'sunken',
                         -textvariable => $$matrix_entry[$row][$col],
                         )->pack(-side => 'left', padx => '2', pady =>
+ '2');
  }
}
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Note that you don't need to keep separate handles around for the three frame widgets, and by using the -textvariable attribute on the Entry widgets, you don't need all the "get()" method calls. Your solution subroutine can then be simpler too, using a loop (or map and join) to print out the matrix values, and using the "new_from_rows" method of Math::MatrixReal to initialize the matrix object.

update: changed from my $nrows=3 ... for my $row (1..$nrows)... -- I realized that for the sake of the Math::MatrixReal calls, the array elements really should start at 0 rather than 1.