diff --git a/src/lib.rs b/src/lib.rs
index 0f6b59f..9f20d13 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -377,9 +377,12 @@ impl Matrix {
             data: self.data.clone(),
         };
 
+        // Inserts indentity matrix
         for i in 0..inverse.rows {
+            // create full of 0 column
             let mut new_column: Vec<Fraction> = vec![Fraction::from(0i64); inverse.rows];
 
+            // at i set to 1
             new_column[i] = Fraction::from(1i64);
 
             inverse.insert_column(inverse.columns - 1, new_column)?;
@@ -393,6 +396,35 @@ impl Matrix {
 
         Ok(inverse)
     }
+
+    pub fn solve_matrix_with_gauss_jordan(
+        &self,
+        solution_matrix: Vec<Fraction>,
+    ) -> Result<Vec<Fraction>, MatrixError> {
+        if self.columns != self.rows {
+            return Err(MatrixError::NotSquared);
+        }
+
+        if solution_matrix.len() != self.columns {
+            return Err(MatrixError::InvalidDataSize);
+        }
+
+        let mut solved_matrix = Matrix {
+            rows: self.rows,
+            columns: self.columns,
+            data: self.data.clone(),
+        };
+
+        solved_matrix.insert_column(self.columns, solution_matrix)?;
+        let solved_matrix = solved_matrix.gauss_jordan_elimination()?;
+
+        let result = solved_matrix
+            .get_column(solved_matrix.columns)?
+            .cloned()
+            .collect();
+
+        Ok(result)
+    }
 }
 
 impl Add for Matrix {