diff --git a/stan/math/prim/fun/rep_matrix.hpp b/stan/math/prim/fun/rep_matrix.hpp
index 8a59ff41af3..efb20628523 100644
--- a/stan/math/prim/fun/rep_matrix.hpp
+++ b/stan/math/prim/fun/rep_matrix.hpp
@@ -47,11 +47,12 @@ inline auto rep_matrix(const T& x, int m, int n) {
  * vector.
  * @tparam Vec An Eigen vector.
  * @param x An Eigen vector. For Row vectors the values are replicated rowwise.
- * and for column vectors the values are repliacated colwise.
+ * and for column vectors the values are replicated colwise.
  * @param n Number of rows or columns.
  */
 template <typename Vec, require_eigen_vector_t<Vec>* = nullptr>
-inline auto rep_matrix(const Vec& x, int n) {
+inline Eigen::Matrix<scalar_type_t<Vec>, -1, -1> rep_matrix(const Vec& x,
+                                                            int n) {
   if constexpr (is_eigen_row_vector<Vec>::value) {
     check_nonnegative("rep_matrix", "rows", n);
     return x.replicate(n, 1);
diff --git a/test/unit/math/prim/fun/rep_matrix_test.cpp b/test/unit/math/prim/fun/rep_matrix_test.cpp
index f92e4d389e3..3ee6ac9c1d9 100644
--- a/test/unit/math/prim/fun/rep_matrix_test.cpp
+++ b/test/unit/math/prim/fun/rep_matrix_test.cpp
@@ -52,3 +52,15 @@ TEST(MathMatrixPrimMat, rep_matrix_row_vec) {
 
   EXPECT_THROW(rep_matrix(rv, -1), std::domain_error);
 }
+
+TEST(MathMatrixPrimMat, rep_matrix_both_ways) {
+  using stan::math::rep_matrix;
+
+  Eigen::Matrix<double, 1, Eigen::Dynamic> rv(3);
+  rv << 1.0, 4.0, 9.0;
+
+  Eigen::Matrix<double, Eigen::Dynamic, 1> v(3);
+  v << 1.0, 4.0, 9.0;
+  Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> x(3, 3);
+  x = true ? rep_matrix(v, 3) : rep_matrix(rv, 3);
+}