How can I find indices of each unique elements in a matrix, in one shot. (efficiently)??

How can I find indices of each unique elements in a matrix, in one shot. (efficiently)?

For explaining i made this simple script

%%Creation of 'mat'
mat = magic(10);
for i=1:10
  mat(mat>(10*i-10) & mat<=10*i)=i;
end

mat_unique = unique(mat(:));   % unique values of 'mat'

%%Finding indices of each unique elements 
%%Below thing I want to do in 1 shot without 'for' loop
%%because in my actual problem 'mat' size is very big.
for i=1:length(mat_unique)
  index(:,i) = find(mat == mat_unique(i))    
end

Answer 1

[Stephen23]

>> [~,idx] = sort(mat(:));
>> reshape(idx,10,10)
ans =
     3     6     7    59    56    53    51     8     4     1
     9    10    16    60    57    54    55    12     5     2
    17    19    25    68    66    62    64    26    13    11
    18    20    34    69    70    63    65    40    14    15
    21    24    43    77    79    71    73    49    23    29
    22    28    58    78    80    72    74    52    27    30
    31    32    67    86    88    81    82    61    36    38
    35    33    76    87    89    85    83    75    37    39
    44    41    90    91    92    99    96    84    46    47
    45    42    94    95    93   100    97    98    50    48