# C program to find determinant of Matrix | C code champ

Mr Coder August 22, 2012 13

C program to find determinant of Matrix : The determinant of a matrix is a number that can be calculated from the matrix. It tells us things about the matrix that are useful in systems of linear equations, in calculus and more. First of all, if you want to calculate the determinant of matrix then your matrix should be an square matrix i.e. MxM , otherwise determinant will not exist.

If you wish to calculate determinant of 3×3 matrix then formula will be something like below :

Say 3×3 matrix is :

Sample 3×3 Matrix

Then its determinant will be like below:

Determinant of 3×3 matrix

`Note : |  |  denotes determinant . That means 3 x 3 matrix has been broken into 3 small determinants`

Now consider an example of 4×4 matrix :

Determinant of 4×4 Matrix

Notice the + – + – pattern (+a… -b… +c… -d…). This is important to remember.

The pattern continues for 5×5 matrices and higher.

Now let us see how to write a C program to find determinant of Matrix MxM . The program will accept the order of matrix i.e. M as input from user and then ask user to enter the values of matrix elements. Then it will calculate the determinant of the matrix and returns the output.

### C program to find determinant of Matrix :

```#include<conio.h>
#include<stdio.h>

int a[20][20],m;
int determinant(int f[20][20],int a);
int main()
{
int i,j;
printf("----------------------------------------------------------------------\n");
printf("-------------------made by C code champ ------------------------------\n");
printf("----------------------------------------------------------------------\n");
printf("\n\nEnter order of matrix : ");
scanf("%d",&m);
printf("\nEnter the elements of matrix\n");
for(i=1;i<=m;i++)
{
for(j=1;j<=m;j++)
{
printf("a[%d][%d] = ",i,j);
scanf("%d",&a[i][j]);
}
}
printf("\n\n---------- Matrix A is --------------\n");
for(i=1;i<=m;i++)
{
printf("\n");
for(j=1;j<=m;j++)
{
printf("\t%d \t",a[i][j]);
}
}
printf("\n \n");
printf("\n Determinant of Matrix A is %d .",determinant(a,m));
getch();
}

int determinant(int f[20][20],int x)
{
int pr,c[20],d=0,b[20][20],j,p,q,t;
if(x==2)
{
d=0;
d=(f[1][1]*f[2][2])-(f[1][2]*f[2][1]);
return(d);
}
else
{
for(j=1;j<=x;j++)
{
int r=1,s=1;
for(p=1;p<=x;p++)
{
for(q=1;q<=x;q++)
{
if(p!=1&&q!=j)
{
b[r][s]=f[p][q];
s++;
if(s>x-1)
{
r++;
s=1;
}
}
}
}
for(t=1,pr=1;t<=(1+j);t++)
pr=(-1)*pr;
c[j]=pr*determinant(b,x-1);
}
for(j=1,d=0;j<=x;j++)
{
d=d+(f[1][j]*c[j]);
}
return(d);
}
}```

We hope you all have enjoyed the C program to find determinant of Matrix. If you have any issues with the above code or logic of above code then ask us in form of comment.

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1. Nidhin September 17, 2012 at 3:20 pm - Reply

Very simple program but powerfull.Thanks pal……….

2. wow gold October 10, 2012 at 10:56 pm - Reply

Itˇs really a nice and helpful piece of info. I am glad that you just shared this helpful info with us. Please keep us up to date like this. Thanks for sharing.

3. Reda Brackin November 6, 2012 at 7:25 pm - Reply

4. sara December 3, 2012 at 9:27 pm - Reply

slt je veux un programme pour calculer det(A)=0, A est une matrice, a un variable . je veux calculer det(A)=0 pour trouver ce variable (je vais tomber sur une polynome de degré 6, et je dois calculer les racines de cette polynome). merci d’avance

5. sara December 4, 2012 at 10:07 am - Reply

i want program to calcul the “valeur propre” d’une matrice 4*4 en utilisant polynome caracteristique

pls i dont knw if you can help write dis same code in c++ bcos am having problems writing it in c++.thanks

7. Crea Torr March 9, 2013 at 9:12 pm - Reply

Can u plz tll me “What is the use of t ,and incrementing it if it not further used in program?”

8. sarath July 6, 2014 at 8:57 am - Reply

Happy to know that u are on our generatiom
all the best & attain peaks…
– visitor™

9. Jalaj Negi September 8, 2014 at 4:12 pm - Reply

/* Little improvement 2 above function – 10×10 is taken instead of 20×20 */

int determinant(int f[10][10], int x)
{
int b[10][10],c[10], i,j,k,s, sign =1, det = 0;

if(2==x)
{
det = f[0][0]*f[1][1] – f[0][1]*f[1][0];
}
else
{
for (i=0;i<x;i++,sign*=-1)
{
for(j=1;j<x;j++)
{
for(s=k=0;k<x;k++)
{
if(i != k)
{
b[j-1][s] = f[j][k];
s++;
}
}
}

det += (sign * f[0][i] * determinant(b,x-1));
}
}

return det;
}

10. xyz September 11, 2014 at 7:28 am - Reply

showing segmentation error wen i pass input matrix of order 100 at line
b[r][s]=f[p][q];

11. gopbis November 11, 2014 at 10:16 am - Reply

12. HAYAL November 18, 2014 at 12:18 pm - Reply

the program is very good thank you for everything

13. Shamte Juma December 11, 2014 at 11:23 am - Reply

program as program does?