c++ - Armadillo: matrix.i(true) vs matrix.i()—one is a logic error, the other isn't? -

the input matrix looks this:

[ 1 2 4 ] [ 4 5 6 ] [ 7 8 9 ] 

(mat1)

wolfram alpha confirms has inverse. using matrix.i() (which means uses fast invert) yields approximately correct result of

[  1.0000 -4.6667  2.6667 ] [ -1.0000  6.3333 -3.3333 ] [  1.0000 -2.0000  1.0000 ] 

(mat2)

but turning slow mode on writing matrix.i(true) causes throw logic_error. any reason that?

reason tried turn on multiplying inverted matrix vector of

[ 15 ] [ 24 ] [ 35 ] 

(mat3)

yields incorrect answer of

[ -3.6667 ] [ 20.3333 ] [  2.0000 ] 

(mat4)

when should this, or

[ -3.6667 ] [  5.3333 ] [  2.0000 ] 

(mat5)

checking before multiplication confirmed input (mat3) correct, leading me believe fast inverse created incorrect matrix output (mat4 instead of mat5).

... think of it, fast inverse correct , there no reason not correct... quandary.

the main question is, written above,

any reason matrix.i(true) causes logic error while matrix.i() doesn't?