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Question
If A =`[[2 -3 -5],[-1 4 5],[1 -3 -4]]` and B =`[[2 -2 -4],[-1 3 4],[1 2 -3]]`
, show that AB = A and BA = B.
Solution
Given : AB=`[[2 -3 -5],[-1 4 5],[1 -3 -4]]` `[[2 -2 -4],[-1 3 4],[1 2 -3]]`
`⇒AB= [[4+3-5 -4-9+10 -8-12+15],[-2-4+5 2+12-10 4+16-15],[2+3-4 -2-9+8 -4-12+12]]`
`⇒AB=[[2 -3 -5],[-1 4 5],[1 -3 -4]]`
⇒AB=A
`BA=[[2 -2 -4],[-1 3 4],[1 -2 -3]]` `[[2 -3 -5],[-1 4 5],[1 -3 -4]]`
`⇒ BA= [[4+2-4 -6-8+12 -10-10+16],[-2-3+4 3+12-12 5+15-16],[2+2-3 -3-8+9 -5-10+12]]`
`⇒BA=[[2 -2 -4],[-1 3 4],[1 -2 -3]]`
⇒BA=B
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