Question

find inverse of a square matrix
2 3 4
4 3 1
1 2 4

Answer 1

2 4 1
3 3 2
4 1 4

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Answer 2

Now given matrix,,

           2  3  4
      
           4  3  1

          1   2  4


for , 2'' (sub matrix)

    2 =(12 - 2 ) i.e 10 ..

in same way repeat for all , i mean get the sub matrix of all.

  for 3,, 16 -1=15
       4,,  8-3  5
       4,,  12 -8 =4
       3,,  8 -4 =4
       1,,  4 -3 =1
       1,, 3 -12 = -9
       2,, 2 - 16 = -14
      4 ,, 6 - 12  =-6



      Now A INVERSE = A dj A
                                      ------------
                                      Det A


 form Adj A =  u apply rule andmake transpose

   i.e..,  +   -  +
            -   +  -
           +   -   +

u get...


     10    -15    5
     -4     4       -1
     -9     14     -6

since Det A = -5

u get , after transposing


     = 1/-5 x   10  -4   -9
                     -15 4    14
                    5    -1    -6

hope it helps U ......   :)