b
(b) $\left| {\,\begin{array}{*{20}{c}}{31}&{37}&{92}\\{31}&{58}&{71}\\{31}&{105}&{24}\end{array}\,} \right|\, = \,\left| {\,\begin{array}{*{20}{c}}{31}&{37}&{92}\\0&{21}&{ - 21}\\0&{47}&{ - 47}\end{array}\,} \right|$;by $\begin{array}{l}{R_3} \to {R_3} - {R_2}\\{R_2} \to {R_2} - {R_1}\end{array}$
= $\left| {\,\begin{array}{*{20}{c}}{31}&{129}&{92}\\0&0&{ - 21}\\0&0&{ - 47}\end{array}\,} \right| = 0; $
(by ${C_2} \to {C_2} + {C_3})$.