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Show that AB = BA, where A = [-23-1-12-1-69-4],B=[13-122-130-1].

Exercise 2.3 | Q 3 | Page 55

QUESTION

Show that AB = BA, where A = [-23-1-12-1-69-4],B=[13-122-130-1].

SOLUTION

AB = [-23-1-12-1-69-4][13-122-130-1]

[-2+6-3-6+6-02-3+1-1+4-3-3+4-01-2+1-6+18-12-18+18+06-9+4]

∴ AB = [100010001]         ...(i)

BA = [13-122-130-1][-23-1-12-1-69-4]

[2-3+63+6-9-1-3+4-4-2+66+4-9-2-2+4-6+0+69+0-93+0+4]

∴ BA = [100010001]       ...(ii)

From (i) and (ii), we get
AB = BA.


HSC Mathematics Full Solution