Singular matrix inversion doesn't produce an Exception as it does for Matrix

[eeshan9815]

julia> A = [0 1; 0 0]
2×2 Array{Int64,2}:
 0  1
 0  0

julia> inv(A)
ERROR: Base.LinAlg.LAPACKException(1)
Stacktrace:
 [1] chklapackerror(::Int64) at ./linalg/lapack.jl:34
 [2] trtrs!(::Char, ::Char, ::Char, ::Array{Float64,2}, ::Array{Float64,2}) at ./linalg/lapack.jl:3291
 [3] inv at ./linalg/triangular.jl:536 [inlined]
 [4] inv(::Array{Int64,2}) at ./linalg/dense.jl:655

julia> A = @SMatrix [0 1; 0 0]
2×2 StaticArrays.SArray{Tuple{2,2},Int64,2,4}:
 0  1
 0  0

julia> inv(A)
2×2 StaticArrays.SArray{Tuple{2,2},Float64,2,4}:
 NaN  -Inf
 NaN   NaN

[andyferris]

This is a rather interesting case: Julia supports inv(0.0) = Inf so I wouldn't necessarily say we have to throw an exception when it's not invertible, if the result is correctly captured by IEEE floating point NaN and Inf... (that is, after all, a LAPACKException so it seems more of an implementation detail maybe?). On the other hand it can be kind-of nice to know when things mess up.

Anyone else have thoughts?

[c42f]

I feel it would be good to throw here for consistency. But for the particularly tiny case of 2x2 we should benchmark to determine the cost of inserting a branch and extra code, I suppose.