Given matrices are
A=⎣⎡143−3122−15⎦⎤ and B=⎣⎡2−131−215−22⎦⎤
Now, AB=⎣⎡143−3122−15⎦⎤⎣⎡2−131−215−22⎦⎤=⎣⎡11419914151621⎦⎤
Determinant of the matrix AB is 1471.
Co-factors are:
a11=(21−64)=−43
a12=−(84−304)=220
a13=(16−19)=−3
a21=−(189−60)=−129
a22=(231−285)=−54
a23=−(44−171)=127
a31=(144−15)=129
a32=−(176−60)=−116
a33=(11−36)=−25
adj(AB)=⎣⎡−43220−3−129−54127129−116−25⎦⎤
adj(AB)=
Then inverse of the matrix AB is,
(AB)−1=14711⎣⎡−43220−3−129−54127129−116−25⎦⎤
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