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Question

If A1=3111565522 and B=122130021, find (AB)1.

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Solution

We know that, (AB)1=B1A1andA1 is known, therefore we proceed to find B1
Here, |B|=∣ ∣122130021∣ ∣=1(30)2(10)2(20)=3+24=10
B1 exists. Cofactors of B are
B11=(30)=3,B12=(10)=1,B13=(20)=2B21=(24=2),B22=10=1,B23=(20)=2B31=(0+6)=6B32=(02)=2,B33=3+2=5
adj(B)=312212625T=326112225
B1=1|B|(adj(B))=11326112225=326112225
Now, (AB)1=B1A1=326112225=3111565522
=930+303+1212310+12315+101+6415+4630+252+1210210+10=935210102


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