If `A=[(2, 3),( 5,-2)]`
, show that `A^(-1)=1/(19)Adot`
Text Solution
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We have given that `A=[(2, 3),( 5,-2)]`
Then we have to proof that `A^(-1)=1/(19)A`
As the determinant of `A`, `|A|=(2xx-2)-(5xx3)=-4-15=-19ne0`
Then to inverse we have to find first adjoint of the matrix A .
Then to find adjoint we find the minors of it =`[[-2,5],[ 3,2]]`
And co-factors=`[((-1)^(1+1)(-2), (-1)^(1+2)(5)),( (-1)^(2+1)(3),(-1)^(2+2)(2))]=[(-2,-5),(-3,2)]`
Then `adj A=[(-2,-3),(-5,2)]`
The inverse of the matrix `A` , `A^(-1)=(1/(|A|))adj A`
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