diff --git a/matrix.hpp b/matrix.hpp
index 6d5a46c..c04b33d 100644
--- a/matrix.hpp
+++ b/matrix.hpp
@@ -3,6 +3,7 @@
 #include "vector.hpp"
 #include <cstdint>
 #include <iostream>
+#include <ostream>
 #include <sstream>
 #include <string>
 class matrix {
@@ -12,6 +13,31 @@ private:
   vector *entries;
   bool err;
   bool augmented = false;
+  // recursive determinant
+  const cnumber rdeterminant(matrix m) const {
+    if (m.get_num_entries() == 2) {
+      cnumber dsum(1, 0);
+      cnumber osum(1, 0);
+      vector diag = m.get_diagonal();
+      vector odiag = m.get_off_diagonal();
+      for (uint64_t i = 0; i < diag.get_dimention(); i++) {
+        dsum = dsum * diag[i];
+        osum = osum * odiag[i];
+      }
+      return dsum - osum;
+    } else {
+      cnumber sum = 0;
+      cnumber sign(1);
+      for (uint64_t i = 0; i < m.entry_dimension; i++) {
+        matrix n = m.remove_first_row_and_column(i);
+	if(i % 2 == 0)
+		sum = sum + (m[0][i] * rdeterminant(n));
+	else
+		sum = sum - (m[0][i] * rdeterminant(n));
+      }
+      return sum;
+    }
+  }
 
 public:
   // Constructors/destructor
@@ -76,15 +102,9 @@ public:
     return n;
   }
   const cnumber determinant() const {
-    cnumber dsum(1, 0);
-    cnumber osum(1, 0);
-    vector diag = this->get_diagonal();
-    vector odiag = this->get_off_diagonal();
-    for (uint64_t i = 0; i < diag.get_dimention(); i++) {
-      dsum = dsum * diag[i];
-      osum = osum * odiag[i];
-    }
-    return dsum - osum;
+    if (this->num_entries != this->entry_dimension)
+      return 0;
+    return rdeterminant(*this);
   }
   // switch row i with row j
   const matrix exchange_row(uint64_t i, uint64_t j) {
@@ -122,6 +142,15 @@ public:
     if (!m.is_invertible()) {
       m.err = true;
     } else {
+      uint64_t num_entries = m.get_num_entries();
+      for (uint64_t i = 0; i < num_entries - 1; i++) {
+        for (uint64_t j = i; j < num_entries; j++) {
+          cnumber ratio = m[j][i] / m[i][i];
+          for (uint64_t k = i; k < num_entries; k++) {
+            m[j][k] = m[j][k] - (ratio * m[i][k]);
+          }
+        }
+      }
     }
     return m;
   }
@@ -153,6 +182,7 @@ public:
     }
     return m;
   }
+  const bool is_broken() const { return this->err; }
   const bool is_diagonal() const {
     bool result = true;
     if (this->num_entries != this->entry_dimension)
@@ -192,6 +222,21 @@ public:
     return m;
   }
 
+  const matrix remove_first_row_and_column(uint64_t column) const {
+    matrix m(this->num_entries - 1, this->entry_dimension - 1);
+    uint64_t add = 0;
+    for (uint64_t i = 1; i < this->num_entries; i++) {
+      for (uint64_t j = 0; j < this->entry_dimension; j++) {
+        if (j != column) {
+          m[i - 1][j - add] = this->get_entry(i)[j];
+        } else {
+          add = 1;
+        }
+      }
+      add = 0;
+    }
+    return m;
+  }
   const matrix rotate() const {
     matrix m = this->transpose();
     matrix n = matrix(m.entry_dimension, m.num_entries);