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Question
Show that the matrices A = `[(1, 2),(3, 1)]`, B = `[(1, -2),(-3, 1)]` satisfy commutative property AB = BA
Solution
A = `[(1, 2),(3, 1)]`, B = `[(1, -2),(-3, 1)]`
AB = `[(1, 2),(3,1)] xx [(1, -2),(-3, 1)]`
= `[(1 - 6, -2 + 2),(3 - 3, - 6 + 1)]`
= `[(-5, 0),(0, -5)]` ...(1)
BA = `[(1, -2),(-3, 1)] xx [(1, 2),(3, 1)]`
= `[(1 - 6, 2 - 2),(-3 + 3, -6 + 1)]`
= `[(-5, 0),(0, -5)]` ...(2)
From (1) and (2) we get
AB = BA.
It satisfy the commutative property.
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