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Question
Let `A = [(1, 0),(2, 1)], B = [(2, 3),(-1, 0)]`. Find `A^2 + AB + B^2`
Solution
`A = [(1, 0),(2, 1)], B = [(2, 3),(-1, 0)]`
`A^2 = A xx A = [(1, 0),(2, 1)] xx [(1, 0),(2, 1)]`
`=[(1 xx 1 + 0 xx 2, 1 xx 0 + 0 xx 1),(2 xx 1 + 1 xx 2, 2 xx 0 + 1 xx 1)] = [(1, 0),(4, 1)]`
`AB = A xx B = [(1, 0),(2, 1)] xx [(2, 3),(-1, 0)]`
`=[(1 xx 2 + 0 xx (-1), 1 xx 3 + 0 xx 0),(2 xx 2 + 1 xx (-1), 2 xx 3 + 1 xx 0)]`
`= [(2, 3),(3, 6)]`
`B^2 = B xx B = [(2, 3),(-1, 0)] xx [(2, 3),(-1, 0)]`
`= [(2 xx 2 + 3 xx (-1), 2 xx 3 + 3 xx 0),((-1)xx2 + 0 xx (-1), -1 xx 3 + 0 xx 0)]`
`= [(1, 6),(-2, -3)]`
`:. A^2 + AB + B^2 = [(1, 0),(4, 1)] + [(2, 3),(3, 6)] + [(1, 6),(-2, -3)]`
`= [(4, 9),(5, 4)]`
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