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A=[(2,0,-1),(5,1,0),(0,1,3)]A^-1=?...

`A=[(2,0,-1),(5,1,0),(0,1,3)]A^-1=?`

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`Let A= [{:(2,0,-1),(5,1,0),(0,1,3):}]`
` Now, A=IA `
`implies[{:(2,0,-1),( 5,1,0),( 0,1,3):}]A^(-1)=[{:(1,0,0),(0,1,0),(0,0,1):}]`
`implies [{:( 1,0,-(1)/(2)),(5,1,0),( 0,1,3):}]A^(-1)=[{:((1)/(2),0,0),(0,1,0),(0,0,1):}]R_(1) to (1)/(2) R_(1)`
`implies [{:( 1,0,-(1)/(2)),(0,1,(5)/(2)),(0,1,3):}]A^(-1)=[{:((1)/(2),0,0),(-(5)/(2),1,0),(0,0,1):}]R_(2) to R_(2) -5R_(1)`
`=[{:(1,0,-(1)/(2)),(0,1,(5)/(2)),(0,0,(1)/(2)):}]A^(-1)=[{:((1)/(2),0,0),(-(5)/(2),1,0),((5)/(2),-1,1):}]R_(3)to R_(3)-R_(2)`
`implies[{:(1,0,-(1)/(2)),(0,1,(5)/(2)),(0,0,1):}]A^(-1)=[{:((1)/(2),0,0),(-(5)/(2) ,1,0),(5,-2,2):}] R_(3) to 2R_(3)`
`implies[{:(1,0,0),(0,1,0),(0,0,1):}]A^(-1)=[{:(3,-1,1),(-15,6,-5),(5,-2,2):}]`
`R_(1) to R_(1) +(1)/(2) R_(3) and R_(2) to R_(2) to R_(2) -(5)/(2) R_(3)`
`implies A^(-1) =[{:(3,-1,1),(-15,6,-5),(5,-2,2):}].`
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