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Question
Find the matrix A, If B =`[(2,1),(0,1)] and B^2 = B+1/2A`
Solution
`B^2 = B+1/2A`
`A = 2 (B^2 - B)`
`B^2 = [(2,1),(0,1)][(2,1),(0,1)]`
= `[(4,+0,2,+1),(0,+0,0,+1)]`
= `[(4,3),(0,1)]`
= `B^2-B = [(4,3),(0,1)]-[(2,1),(0,1)]`
= `[(2,2),(0,0)]`
`A = 2(B^2 - B)`
= `2[(2,2),(0,0)]=[(4,4),(0,0)]`
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