program lr;

type
  mtr = array[0..9, 0..9] of real;

const
  eps = 0.00001;{ all numbers less than eps are equal to zero }

var
  a,b,d:mtr;
  w,i,j,s1,s2,n:byte;

procedure Trans(m1:mtr;var m2:mtr);
var
  i,j:byte;
begin
 for i:=0 to n-1 do
  for j:=0 to n-1 do
   m2[i,j]:=m1[j,i];
end;

function Scal(a:mtr; st,sb:byte):real;
var
  i:byte;
  s:real;
begin
  s:=0;
  for i:=0 to n-1 do
   s:=s+a[st-1,i]*a[i,sb-1];
  scal:=s;
end;

procedure PrintMatr(m:mtr);
var
  i,j:integer;
begin
  for i:=0 to n-1 do
  begin
    for j:=0 to n-1 do
      write(m[i,j]:8:3);
    writeln;
  end;
end;

procedure Inversion(m:mtr; var c:mtr);
var
 m1,e:mtr;
 i,j,k,p,r:byte;
 Q,Dummy:real;
begin
 for i:=0 to n-1 do
  for j:=0 to n-1 do
   begin
    m1[i,j]:=m[i,j];
    e[i,j]:=0;
   end;
 for i:=0 to n-1 do e[i,i]:=1;
 {Avers}
 for k:=0 to n-1 do
  begin
   Q:=m1[k,k];
   if Abs(Q)<eps then
    begin
     Writeln('No solution!');
     Readln;
     Halt;
    end
   else
    begin
     for j:=0 to n-1 do
      begin
       m1[k,j]:=m1[k,j]/Q;
       e[k,j]:=e[k,j]/Q;
      end;
     for i:=k+1 to n-1 do
      begin
       Q:=m1[i,k];
       if Abs(Q)<eps then
        m1[i,k]:=0
       else
        for j:=0 to n-1 do
         begin
          m1[i,j]:=m1[i,j]/Q;
          e[i,j]:=e[i,j]/Q;
          m1[i,j]:=m1[k,j]-m1[i,j];
          e[i,j]:=e[k,j]-e[i,j];
         end;
      end;
    end;
  end;

 {Revers}
 for k:=n-1 downto 0 do
  begin
   Q:=m1[k,k];
   if Abs(Q)<eps then
    begin
     Writeln('No solution!');
     Readln;
     Halt;
    end
   else
    begin
     for j:=n-1 downto 0 do
      begin
       m1[k,j]:=m1[k,j]/Q;
       e[k,j]:=e[k,j]/Q;
      end;
     if k>0 then
      begin
       for i:=k-1 downto 0 do
        begin
         Q:=m1[i,k];
         if Abs(Q)<eps then
          m1[i,k]:=0
         else
          for j:=n-1 downto 0 do
           begin
            m1[i,j]:=m1[i,j]/Q;
            e[i,j]:=e[i,j]/Q;
            m1[i,j]:=m1[i,j]-m1[k,j];
            e[i,j]:=e[i,j]-e[k,j];
           end;
        end;
      end;
    end;
  end;
 for i:=0 to n-1 do
  for j:=0 to n-1 do
   c[i,j]:=e[i,j];
end;

procedure MultMatr(a,b:mtr; var c:mtr);
var
  i,j,k:byte;
  s:real;
begin
  for i:=0 to n-1 do
    for j:=0 to n-1 do
    begin
      s:=0;
      for k:=0 to n-1 do
       s:=s+a[i,k]*b[k,j];
      c[i,j]:=s;
    end;
end;

Begin
 repeat
  write('Enter the matrix size from 2 to 10, n = ');
  readln(n);
 until n in [2..10];
 randomize;
 for i:=0 to n-1 do
  for j:=0 to n-1 do a[i,j]:=1+random(10);
 Repeat
  writeln;
  writeln('Choose the action:');
  writeln('1 - Matrix transposition');
  writeln('2 - Scalar product of string and column');
  writeln('3 - Inverse matrix');
  writeln('4 - Quit');
  repeat
    readln(w);
  until w in [1..4];
  case w of
    1:
      begin
       Trans(a,b);
       Writeln('Initial matrix:');
       PrintMatr(a);
       Writeln;
       Writeln('Transposed matrix:');
       PrintMatr(b);
      end;
    2:
      begin
       repeat
        Writeln('Initial matrix:');
        PrintMatr(a);
        Writeln;
        write('Enter the string number from 1 to ', n, ' s1 = ');
        readln(s1);
        if (s1>n) then
         writeln('String with this number does not exist');
       until s1 in [1..n];
       repeat
        write('Enter the column number from 1 to ', n, ' s2 = ');
        readln(s2);
        if (s2>n) then
         writeln('Column with this number does not exist');
        until s2 in [1..n];
        writeln('Scalar product of string ',s1,' and column ', s2, ' = ', Scal(a,s1,s2):0:3);
      end;
    3:
      begin
       Inversion(a,b);
       Writeln('Initial matrix:');
       PrintMatr(a);
       Writeln;
       Writeln('Inverse matrix:');
       PrintMatr(b);
       Writeln;
       Writeln('Test. Product of initial and inverse matrix:');
       MultMatr(a,b,d);
       PrintMatr(d);
      end;
    end;
 Until w=4;
End.