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If A={:[(1,4),(-2,5)]:}andB={:[(-6,-1),(...

If `A={:[(1,4),(-2,5)]:}andB={:[(-6,-1),(-8,2)]:}`, then AB + BA = ________ .

A

`{:[(-42,22),(40,10)]:}`

B

`{:[(-42,-22),(-40,-10)]:}`

C

`{:[(-42,22),(-40,10)]:}`

D

`{:[(42,22),(40,10)]:}`

Text Solution

Verified by Experts

The correct Answer is:
B
Given `A={:[(1,4),(-2,5)]:}andB={:[(-6,-1),(-8,2)]:}`
`AB={:[(1,4),(-2,5)]:}{:[(-6,-1),(-8,2)]:}`
`={:[(1xx-6+4xx-8,1xx-1+4xx2),(-2x-6+5x-8,-2xx-1+5xx2)]:}`
`={:[(-6-32,-1+8),(+12-40,2+10)]:}={:[(-38,7),(-28,12)]:}`.
`BA={:[(-6,-1),(-8,2)]:}{:[(1,4),(-2,5)]:}`
`={:[(-6+2,-24-5),(-8-4,-32+10)]:}`
`={:[(-4,-29),(-12,-22)]:}`.
`AB+BA={:[(-38-4,7-29),(-28-12,12-22)]:}`
`={:[(-42,-22),(-40,-10)]:}`.
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