How do you find the inverse of #A=##((3, 2), (4, 5))#?

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Answer 1 · 2016-11-25T07:12:46

The inverse is #A^(-1)=( (5/7,-2/7), (-4/7,3/7) ) #

To calculate the inverse of a matrix, verify that the determinant is #!=0#

Det A=# | (3,2), (4,5) | =3*5-2*4=15-8=7#

As # DetA !=0#, the inverse exists.

Let's calculate the minors cofactor

Minor cofactor is # ( (5,-4), (-2,3) )#

Then we take the tranpose, #( (5,-2), (-4,3) )#

The inverse is #A^(-1)=1/7( (5,-2), (-4,3) ) #

#A^(-1)=( (5/7,-2/7), (-4/7,3/7) ) #

Verification

#A*A^(-1)=( (3,2), (4,5) ) *( (5/7,-2/7), (-4/7,3/7) ) #

#=( (1,0), (0,1) )=I#