Formula for Complex Matrices

I don't understand.  In particular the use of the MINVERSE inside which is what I think is causing these whole number complex numbers to produce fractional values.  This doesn't appear to be a 'simple' matrix multiplication.  That said I made some tweaks to your formula to isolate the LAMBDA portion of the formula and also simplified some of the part inside:

=LET(matrix, A1:C3, coef, E1:E3,
iMMULT, LAMBDA(mat,coef,IFERROR(
   BYROW(
     TRANSPOSE(
       WRAPROWS(
         LET(
           re, MAP(mat, IMREAL),
           im, MAP(mat, IMAGINARY),
           MMULT(MINVERSE(HSTACK(VSTACK(re, im), VSTACK(-im, re))),
                 VSTACK(MAP(coef, IMREAL), MAP(coef, IMAGINARY)))
         ), ROWS(mat)
       )
     ), LAMBDA(a, COMPLEX(TAKE(a,, 1), TAKE(a,, -1)))),
   "Singular Matrix")),
iMMULT(matrix,coef))

note how lines 2-14 are a single LAMBDA function you can pull out and use separately.

also note how you can simplify the MAP functions on lines 7,8,and 10

that all said I did a variation for the matrix multiplication I'm used to:

=LET(matrix, A1:C3, coef, E1:E3,
iMMULT, LAMBDA(mat,coef,[complex_format],
         LET(
           imFormat, IF(ISOMITTED(complex_format),1,complex_format),
           rM, MAP(mat, IMREAL),
           iM, MAP(mat, IMAGINARY),
           rC, MAP(coef, IMREAL),
           iC, MAP(coef, IMAGINARY),
           out, MMULT(HSTACK(rM, iM),
                 HSTACK(VSTACK(rC,-iC),VSTACK(iC,rC))),
           IF(imFormat,BYROW(out,LAMBDA(a,COMPLEX(TAKE(a,, 1), TAKE(a,, -1)))),out)
     )),
iMMULT(matrix,coef))

I also included an optional variable [complex_format] that if TRUE or empty will return the values as complex numbers or if FALSE then will leave them as 2 columns (i.e. if further calculations might be preferred)

here is the sheet showing a simple 3x3 with 3 coefficients followed by your formula in col H, my modification of your formula in I and then my version in J: