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show that(AB)1=C1 A1

If,A=[2310];B=[1201]show that (AB)1=B1 A1

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Solution:

AB=[2310][1201]AB=[2712]|AB|=[2712]=30

(AB)1 exists,

Adj(AB)=(2712)(AB)1=13(2712)(AB)1=13(2712)........(1)

B=(1201)|B|=|1201|=10

AdjB=(1201)

B1=11(12 01)A=[2310]|A=|2310∣=30

AdjB=(1201)

B1=11(1201)

A=[2310]|A|2310∣=30

AdjA=[0312]

A1=13[0312]

B1 A1=11[1201]×13[0312]

B1 A1=13[1201][0312]

B1 A1=13[2712]........(2)

From (i) and (ii), (AB)1=B1 A1

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