Find the values of a\ a n d\ b if A=B , ...

Find the values of `a\ a n d\ b` if `A=B` , where `A=[a+4 3b8-6]` , `B=[2a+2b^2+2 8b^2-56]`

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We h ave `A=[{:( a+4,3b) ,( 8,-6):}]_(2xx2)"and" B=[{:(2a+2,b^(2)+2),( 8,b^(2)-5b):}]_(2xx2)`
Also, A=B
By equality of matrices we know that each element of A is equal to the corresponding element of B, that is `a_(ij)=b_(ij)` for all i and j.
`a_(11)=b_(11)rArra+4=2a+2rArra=2`
`a_(12)=b_(12)rArr3bj=b^(2)+2rArrb^(2)=3b-2`
and `a_(22)=b_(22)rArr-6=b^(2)-5b [because b^(2)=3b-2]`
`rArr -6=3b-2-5b`
`rArr 2b=4rArrb=2`
`therefore a=2` and b=2

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