Why is this wrong when I solve for finding the inverse of the matrix by using gauss jordan elimination?

Question

#[(2,3),(4,5)]|[(1,0),(0,1)] #

#R_2-2R_1->[(2,3),(0,-1)]|[(1,0),(-2,1)]#

#R_1-R_2->[(2,2),(0,-1)]|[(3,-1),(-2,1)]#

#1/2R_1->[(1,1),(0,-1)]|[(3/2,-1/2),(-2,1)]#

#R_1+R_2->[(1,0),(0,-1)]|[(-1/2,1/2),(-2,1)]#

#-R_2->[(1,0),(0,1)]|[(-1/2,1/2),(2,-1)]#

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Answer 1 · 2017-08-21T05:36:54

#[(2,3),(4,5)]|[(1,0),(0,1)] #

#R_2-2R_1->[(2,3),(0,-1)]|[(1,0),(-2,1)]#

#R_1-R_2->[(2,\color(red)4),(0,-1)]|[(3,-1),(-2,1)]#

#1/2R_1->[(1,\color(red)2),(0,-1)]|[(3/2,-1/2),(-2,1)]#

#R_1+\color(red)2R_2->[(1,0),(0,-1)]|[(-5/2,3/2),(-2,1)]#

#-R_2->[(1,0),(0,1)]|[(-5/2,3/2),(2,-1)]#