HSC Arts 12th Board ExamMaharashtra State Board
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# Find (AB)-1 if A=[(1,2,3),(1,-2,-3)], B=[(1,-1),(1,2),(1,-2)] - HSC Arts 12th Board Exam - Mathematics and Statistics

ConceptMatrices Inverse by Elementary Transformation

#### Question

Find (AB)-1 if

A=[(1,2,3),(1,-2,-3)], B=[(1,-1),(1,2),(1,-2)]

#### Solution

A=[(1,2,3),(1,-2,-3)], B=[(1,-1),(1,2),(1,-2)]

AB=[(1,2,3),(1,-2,-3)][(1,-1),(1,2),(1,-2)]

= [[6,-3],[-4,1]]

(AB)^-1(AB)=I

(AB)^-1[[6,-3],[-4,1]]=[[1,0],[0,1]]

"Using "R_1 -> 1/6R_1

(AB)^-1[[1,-1/2],[-4,1]]=[[1/6,0],[0,1]]

"Using " R_2 ->R_2+4R_1

(AB)^-1[[1,-1/2],[0,-1]]=[[1/6,0],[2/3,1]]

"using "R_2->(-1)R_2

(AB)^-1[[1,-1/2],[0,1]]=[[1/6,0],[-2/3,-1]]

"Using " R_1->R_1+(1/2)R_2

(AB)^-1[[1,0],[0,1]]=[[-1/6,-1/2],[-2/3,-1]]

(AB)^-1I=[[-1/6,-1/2],[-2/3,-1]]

(AB)^-1=[[-1/6,-1/2],[-2/3,-1]]

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#### APPEARS IN

2015-2016 (March) (with solutions)
Question 1.2.1 | 2.00 marks

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Solution Find (AB)-1 if A=[(1,2,3),(1,-2,-3)], B=[(1,-1),(1,2),(1,-2)] Concept: Matrices - Inverse by Elementary Transformation.
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