Question 7, Exercise 2.3
Solutions of Question 7 of Exercise 2.3 of Unit 02: Matrices and Determinants. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan.
Question 7(i)
Verify that (AB)−1=B−1A−1 if A=[2186] and B=[3202].
Solution.
Given: A=[2186]|A|=12−8=4A−1=14[6−1−82]=[64−14−8424]=[32−14−212] B=[3202]|B|=(3⋅2)−(2⋅0)=6B−1=16[2−203]=[26−26036]=[13−13012] AB=[2186][3202]=[(2⋅3+1⋅0)(2⋅2+1⋅2)(8⋅3+6⋅0)(8⋅2+6⋅2)]=[662428]|AB|=(6⋅28)−(6⋅24)=168−144=24(AB)−1=124[28−6−246]=[2824−624−2424624]=[76−14−114] B−1A−1=[13−13012][32−14−212]B−1A−1=[(12+23)(−112−16)−114]=[76−14−114] (AB)−1=[76−14−114]B−1A−1=[76−14−114] Therefore, (AB)−1=B−1A−1 is verified for the given matrices A and B.
Question 7(ii)
Verify that (AB)−1=B−1A−1 in each of the following A=[1112−1121−3] and B=[3−2321−14−32].
Solution.
Do yourself.
Question 7(iii)
Verify that (AB)−1=B−1A−1 in each of the following A=[2−i612i−i16] and B=[312101011]
Solution.
Question 7(iv)
Verify that (AB)−1=B−1A−1 in each of the following A=[1251−1−123−1] and B=[234102013]
Solution.
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