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Let A={:[(1,2),(3,4)]:},B={:[(-1,-2),(-4...

Let `A={:[(1,2),(3,4)]:},B={:[(-1,-2),(-4,-3)]:}`, find AB and BA.

Text Solution

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`A={:[(1,2),(3,4)]:},B={:[(-1,-2),(-4,-3)]:}`
Now,
`AB={:[(1,2),(3,4)]:}{:[(-1,-2),(-4,-3)]:}`
`={:[(1xx(-1)+2xx(-4),1xx(-2)+2xx(-3)),(3xx(-1)+4xx(-4),3xx(-2)+4xx(-3))]:}`
`={:[(-1-8,-2-6),(-3-16,-6-12)]:}`
`={:[(-9,-8),(-19,-18)]:}`
Now,
`BA={:[(-1,-2),(-4,-3)]:}{:[(1,2),(3,4)]:}`
`={:[(-1xx1+-2xx3,-1xx2+-2xx4),(-4xx1+-3xx3,-4xx2+-3xx4)]:}`
`={:[(-7,-10),(-13,-20)]:}`
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