Here's a crappy little library I wrote to do matrix math in C because why not

main.c

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#ifdef DEBUG
#   undef DEBUG
#   define DEBUG(fmt, ...) fprintf(stderr, "%s:%d:%s: " fmt "\n", __FILE__, __LINE__, __func__, __VA_ARGS__)
#else
#   define DEBUG(fmt, ...)
#endif

typedef struct {
    float *elements;
    int rows; // Height
    int cols; // Width
} Matrix;

Matrix *Matrix_new(int r, int c) {
    Matrix *m = (Matrix*)malloc(sizeof(Matrix));
    m->rows = r;
    m->cols = c;
    m->elements = (float*)malloc(sizeof(float)*r*c);
    return m;
}
void Matrix_free(Matrix *m) {
    free(m->elements);
    free(m);
}

void Matrix_printCol(Matrix * self, int col) {
    for(int i = 0; i < self->rows; i++ ){
        printf("| % 3.4f |\n", self->elements[i*self->cols+col]);
    }
}
void Matrix_printRow(Matrix * self, int row) {
    printf("| ");
    for(int i = 0; i < self->cols; i++ ){
        printf("% 3.4f ", self->elements[row*self->cols+i]);
    }
    printf("|\n");
}

//Returns a new matrix
Matrix *Matrix_multiply(Matrix *a, Matrix *b) {
    // Check if the matrices have the correct dimensions
    if(a->cols != b->rows) return NULL;
    Matrix *result = Matrix_new(a->rows, b->cols);

    // I'm adding these together and dividing by two here because I don't like
    // preferring one of these over the other
    int m = (a->cols + b->rows) / 2;

    // avoid type {a,b,result}->elements a thousand times
    float *A = a->elements,
          *B = b->elements,
          *R = result->elements;

    //A whopping THREE nested loops! YEAH!
    for(int y = 0; y < result->rows; y++) {
        for(int x = 0; x < result->cols; x++) {
            result->elements[y*result->cols + x] = 0;
            for(int i = 0; i < m; i++) {
                R[y*result->cols + x] += 
                    A[y*a->cols+i] * B[i*b->cols+x];
            }
        }
    }
    return result;
}

void Matrix_print(Matrix *self) {
    for(int y = 0; y < self->rows; y++) {
        printf("| ");
        for(int x = 0; x < self->cols; x++) {
            printf("% 9.4f ", self->elements[y*self->cols+x]);
        }
        printf("|\n");
    }
}

int main() {
    float A[] = {
        1, 2, 3, 4,
        5, 6, 7, 8,
    };
    float B[] = {
        1, 2,// 3, 4,
        5, 6,// 7, 8,
        9,10,//11,12,
       13,14,//15,16
    };

    Matrix *a = Matrix_new(2,4);
    DEBUG("Created a %dx%d matrix", a->rows, a->cols);
    memcpy(a->elements, A, sizeof(float)*2*4);

    Matrix *b = Matrix_new(4,2);
    DEBUG("Created a %dx%d matrix", a->rows, a->cols);
    memcpy(b->elements, B, sizeof(float)*4*2);

    printf("Matrix A is: \n");
    Matrix_print(a);
    printf("Matrix B is: \n");
    Matrix_print(b);
    printf("\nAnd, with their powers combined, C is: \n");
    
    Matrix *c = Matrix_multiply(a, b);
    if(!c) {
        printf("Oh no! Your matrices aren't in the correct dimensions(Or, something exploded)\n");
    }else {
        Matrix_print(c);
        
        Matrix_free(c);
    }
    Matrix_free(b);
    Matrix_free(a);
    return 0;
};

Makefile

main: main.c
	gcc -o main main.c