Test SingularException throw for naivesub (#36331)

Author: kshyatt

stdlib/LinearAlgebra/test/bidiag.jl

@@ -232,6 +232,10 @@ Random.seed!(1)
             @test_throws DimensionMismatch transpose(T) \ offsizemat
             @test_throws DimensionMismatch T' \ offsizemat
 
+            if elty <: BlasReal
+                @test_throws SingularException LinearAlgebra.naivesub!(Bidiagonal(zeros(elty, n), ones(elty, n-1), :U), rand(elty, n))
+                @test_throws SingularException LinearAlgebra.naivesub!(Bidiagonal(zeros(elty, n), ones(elty, n-1), :L), rand(elty, n))
+            end
             let bb = b, cc = c
                 for atype in ("Array", "SubArray")
                     if atype == "Array"