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If A = `[(2, -1),(3, -2),(4, 1)] "and B" = [(0, 3, -4),(2, -1, 1)]`, verify that (BA)^{T} = A^{T}B^{T}.

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#### Solution

BA = `[(0, 3, -4),(2, -1, 1)][(2, -1),(3, -2),(4, 1)]`

= `[(0 + 9 - 16, 0 - 6 - 4),(4 - 3 + 4, -2 + 2 + 1)]`

∴ BA = `[(-7, -10),(5, 1)]`

∴ (BA)^{T} = `[(-7, 5),(-10, 1)]` ...(i)

A^{T}B^{T} = `[(2, 3, 4),(-1, -2, 1)][(0, 2),(3, - 1),(-4, 1)]`

= `[(0 + 9 - 16, 4 - 3 + 4),(0 - 6 - 4, -2 + 2 + 1)]`

= `[(-7, 5),(-10, 1)]` ...(ii)

From (i) and (ii)

(BA)^{T} = A^{T}B^{T}.

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