diff --git a/src/det.jl b/src/det.jl
index 66cd8dce..c2593b22 100644
--- a/src/det.jl
+++ b/src/det.jl
@@ -1,13 +1,42 @@
-function LinearAlgebra.det(M::Matrix{<:AbstractPolynomialLike})
-    m = size(M)[1]
-    if m > 2
-        return sum(
-            (-1)^(i - 1) * M[i, 1] * LinearAlgebra.det(M[1:end.!=i, 2:end]) for
-            i in 1:m
-        )
-    elseif m == 2
-        return M[1, 1] * M[2, 2] - M[2, 1] * M[1, 2]
+# Scalar determinant, used for recursive computation of the determinant
+LinearAlgebra.det(p::AbstractPolynomialLike{<:Number}) = p
+
+element_det(e) = LinearAlgebra.det(e)*one(Int8)
+
+# Matrix determinant by cofactor expansion, adapted from
+# `LinearAlgebraX.cofactor_det`.
+
+function det_impl(A::AbstractMatrix{T}) where {T}
+    r = (first ∘ size)(A)
+    if 1 < r
+        total = (element_det ∘ zero)(T)
+        for i ∈ Base.OneTo(r)
+            a = element_det(A[i, 1])
+            if !iszero(a)
+                ii = Base.OneTo(r) .!= i
+                jj = 2:r
+                B = A[ii, jj]
+                sign = let o = one(Int8)
+                    iseven(i) ? -o : o
+                end
+                total += sign * a * det_impl(B)
+            end
+        end
+        total
+    elseif isone(r)
+        element_det(A[1, 1])
     else
-        return M[1, 1]
+        error("unexpected")
+    end
+end
+
+collect_if_not_already_matrix(m::Matrix) = m
+collect_if_not_already_matrix(m::AbstractMatrix) = collect(m)
+
+function LinearAlgebra.det(m::AbstractMatrix{<:AbstractPolynomialLike})
+    if 0 < LinearAlgebra.checksquare(m)
+        (det_impl ∘ collect_if_not_already_matrix)(m)
+    else
+        (element_det ∘ one ∘ eltype)(m)
     end
 end