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Question
If A = `[(-1, 3),(2, 4)], B = [(2, -3),(-4, -6)]` find the matrix AB + BA.
Sum
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Solution
A = `[(-1, 3),(2, 4)]`
B = `[(2, -3),(-4, -6)]`
AB = `[(-1, 3),(2, 4)] xx [(2, -3),(-4, -6)]`
= `[(-1 xx 2 + 3 xx (-4), -1 xx (-3) + 3 xx (-6)),(2 xx 2 + 4 xx (-4), 2 xx (-3) + 4 xx (-6))]`
= `[(-2 - 12, 3 - 18),(4 - 16, -6 - 24)]`
= `[(-14, -15),(-12, -30)]`
BA = `[(2, -3),(-4, -6)] xx [(-1, 3),(2, 4)]`
= `[(2 xx (-1) + (-3) xx 2, 2 xx 3 + (-3) xx 4),(-4 xx (-1) + (-6) xx 2, -4 xx 3 + (-6) xx 4)]`
= `[(-2 - 6, 6 - 12),(4 - 12, -12 - 24)]`
= `[(-8, -6),(-8, -36)]`
∴ AB + BA
= `[(-14, -15),(-12, -30)] + [(-8, -6),(-8, -36)]`
= `[(-14 + (-8), -15 + (-6)),(-12 + (-8), -30 + (-36))]`
= `[(-22, -21),(-20, -66)]`
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