We present the matrix representation for our Twist & Shift pitch transformations (T&S) that define the underlying space group symmetry of the guitar fretboard. The basic matrix is the set of pitches belonging to all 6 strings within any 6-fret interval. A key point is that this pitch-matrix remains invariant under T&S transformations. This hidden symmetry determines such things as chord constellations, paths between enharmonic notes, and the relative position of individual notes within any constellation. T&S helps guitarists understand how the fretboard (matrix) processes music differently from single-note (vector) instruments like the piano and saxophone.