Calculate determinant of a matrix with dimension 3x3

Question

I would like to ask you how to implement the following algorithm for calculating the determinant of a 3x3 matrix:

1. Saving the matrix in a one dimensional array
2. every 9 elements in the array form a matrix
3. send the one dimensional array to kernel
4. every thread finds the determinant of on matrix (array of 9 elements) I would like to ask how can I improve the code below in order to accomplish this exact task? The idea is to save all of the calculated determinants in an output array c with size/9 number of elements.

#include "cuda_runtime.h"
#include "device_launch_parameters.h"

#include <stdio.h>
//method for calculating the determinant of a matrix (3rd) -> calculateMatrixWithCuda
cudaError_t calculateMatrixWithCuda(int *c, const int *a, const int *b, unsigned int size);

//method for sending to kernel 
__global__ void calculateDeterminantOfAMatrixKernel(int *c, const int *a, const int *b)
{
    int i = threadIdx.x;
   //writing the extensive logic here....


}

int main()
{
    //setting up value of the array size, each matrix with dimension 3x3 -> 45 elements in total 
    const int arraySize = 9*5;
    //on the next lines - the matrices follow - 5 in total 
    const int matrix[arraySize] = {
        34,23,245,231,345,235,2,8,43,
        33,990,48,84,38,384,23,40,4,
        67,33,356,8,7,34,43,656,345,
        8,12,65,45,567,78,65,67,8,
        90,567,34,67,756,767,457,74,66
    };
    //array for storing the result of the operation 
    int c[arraySize/9] = { 0 };

    // Add vectors in parallel.
    cudaError_t cudaStatus = calculateMatrixWithCuda(c, a, b, arraySize);
    if (cudaStatus != cudaSuccess) {
        fprintf(stderr, "calculateDeterminantWithCuda failed!");
        return 1;
    }

    printf("{1,2,3,4,5} + {10,20,30,40,50} = {%d,%d,%d,%d,%d}\n",
        c[0], c[1], c[2], c[3], c[4]);

    // cudaDeviceReset must be called before exitъing in order for profiling and
    // tracing tools such as Nsight and Visual Profiler to show complete traces.
    cudaStatus = cudaDeviceReset();
    if (cudaStatus != cudaSuccess) {
        fprintf(stderr, "cudaDeviceReset failed!");
        return 1;
    }

    return 0;
}

// Helper function for CUDA to add vectors in parallel.
cudaError_t addWithCuda(int *c, const int *a, const int *b, unsigned int size)
{
    int *dev_a = 0;
    int *dev_b = 0;
    int *dev_c = 0;
    cudaError_t cudaStatus;

    // Choose which GPU to run on, change this on a multi-GPU system.
    cudaStatus = cudaSetDevice(0);
    if (cudaStatus != cudaSuccess) {
        fprintf(stderr, "cudaSetDevice failed!  Do you have a CUDA-capable GPU installed?");
        goto Error;
    }

    // Allocate GPU buffers for three vectors (two input, one output)    .
    cudaStatus = cudaMalloc((void**)&dev_c, size * sizeof(int));
    if (cudaStatus != cudaSuccess) {
        fprintf(stderr, "cudaMalloc failed!");
        goto Error;
    }

    cudaStatus = cudaMalloc((void**)&dev_a, size * sizeof(int));
    if (cudaStatus != cudaSuccess) {
        fprintf(stderr, "cudaMalloc failed!");
        goto Error;
    }

    cudaStatus = cudaMalloc((void**)&dev_b, size * sizeof(int));
    if (cudaStatus != cudaSuccess) {
        fprintf(stderr, "cudaMalloc failed!");
        goto Error;
    }
    // Copy input vectors from host memory to GPU buffers.
    cudaStatus = cudaMemcpy(dev_a, a, size * sizeof(int), cudaMemcpyHostToDevice);
    if (cudaStatus != cudaSuccess) {
        fprintf(stderr, "cudaMemcpy failed!");
        goto Error;
    }

    cudaStatus = cudaMemcpy(dev_b, b, size * sizeof(int), cudaMemcpyHostToDevice);
    if (cudaStatus != cudaSuccess) {
        fprintf(stderr, "cudaMemcpy failed!");
        goto Error;
    }

    // Launch a kernel on the GPU with one thread for each element.
    addKernel<<<1, size>>>(dev_c, dev_a, dev_b);

    // Check for any errors launching the kernel
    cudaStatus = cudaGetLastError();
    if (cudaStatus != cudaSuccess) {
        fprintf(stderr, "addKernel launch failed: %s\n", cudaGetErrorString(cudaStatus));
        goto Error;
    }
    
    // cudaDeviceSynchronize waits for the kernel to finish, and returns
    // any errors encountered during the launch.
    cudaStatus = cudaDeviceSynchronize();
    if (cudaStatus != cudaSuccess) {
        fprintf(stderr, "cudaDeviceSynchronize returned error code %d after launching calculateMatrixKernel!\n", cudaStatus);
        goto Error;
    }

    // Copy output vector from GPU buffer to host memory.
    cudaStatus = cudaMemcpy(c, dev_c, size * sizeof(int), cudaMemcpyDeviceToHost);
    if (cudaStatus != cudaSuccess) {
        fprintf(stderr, "cudaMemcpy failed!");
        goto Error;
    }
//free the resources 
Error:
    cudaFree(dev_c);
    cudaFree(dev_a);
    cudaFree(dev_b);
    
    return cudaStatus;
}