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Find the inverase of A=[{:(5,-1),(1,1):}...

Find the inverase of A`=[{:(5,-1),(1,1):}]`by using elementary row transformation.

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The correct Answer is:
N/a
we know that A=IA
`implies [{:(5,-1),(1,1):}]=[{:(1,0),(0,1):}]A`
`implies [{:(1,-(1)/(5)),(1,1):}]=[{:((1)/(5),0),(0,1):}]A(R_(1)to (1)/(5)R_(1))`
`implies [{:(1,-(1)/(5)),(0,(6)/(5)):}]=[{:((1)/(5),0),(-(1)/(5),1):}]A(R_(2)to R_(2)-R_(1))`
`implies [{:(1,-(1)/(5)),(0,1):}]=[{:((1)/(5),0),(-(1)/(6),(5)/(6)):}]A(R_(2)to (5)/(6)R_(2))`
`[{:(1,0),(0,1):}]=[{:((1)/(6),(1)/(6)),(-(1)/(6),(5)/(6)):}]A(R_(1)top R_(1)+(1)/(5)R_(2))`
`implies A^(-1)=[{:((1)/(6),(1)/(6)),(-(1)/(6),(5)/(6)):}]=(1)/(6)[{:(1,1),(-1,5):}]`.
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