diff --git a/matrix.hpp b/matrix.hpp
index bdf8ba3..3f844af 100644
--- a/matrix.hpp
+++ b/matrix.hpp
@@ -1,5 +1,7 @@
 #pragma once
+#include "cnumber.hpp"
 #include "vector.hpp"
+#include <cstdint>
 #include <iostream>
 #include <sstream>
 #include <string>
@@ -73,14 +75,40 @@ public:
     if (!m.is_invertible()) {
       m.err = true;
     } else {
-      for (uint64_t i = 0; i < m.get_num_entries(); i++) {
-      }
     }
     return m;
   }
+
+  // switch row i with row j
+  const matrix exchange_row(uint64_t i, uint64_t j) {
+	  matrix m = *this;
+	  vector v = m.get_entry(i);
+	  m[i] = m[j];
+	  m[j] = v;
+	  return m;
+  }
+  // subtract row i from row j
+  const matrix subtract_row(uint64_t i, uint64_t j, cnumber multiplier = 1) {
+	  matrix m = *this;
+	  m[j] = m[j] - (m.multiply_row(i, multiplier)[i]);
+	  return m;
+  }
+  // add row i to row j
+  const matrix add_row(uint64_t i, uint64_t j, cnumber multiplier = 1) {
+	  matrix m = *this;
+	  m[j] = m[j] + (m.multiply_row(i, multiplier)[i]);
+	  return m;
+  }
+
+  // Multiply row by z
+  const matrix multiply_row(uint64_t i, cnumber z) {
+	  matrix m = *this;
+	  m[i] = m[i] * z;
+	  return m;
+  }
   const vector get_entry(uint64_t index) const { return this->entries[index]; }
 
-  const vector get_row(uint64_t index) const {
+  const vector get_column(uint64_t index) const {
     vector v(this->entry_dimension);
     for (uint64_t j = 0; j < this->entry_dimension; j++) {
       v[j] = this->entries[j][index];
@@ -246,7 +274,7 @@ public:
     }
     for (uint64_t i = 0; i < this->entry_dimension; i++) {
       for (uint64_t j = 0; j < this->entry_dimension; j++) {
-        n[i][j] = this->get_entry(i) * m.get_row(j);
+        n[i][j] = this->get_entry(i) * m.get_column(j);
       }
     }