How do you find the inverse?

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Answer 1 · 2017-12-09T08:02:36

The inverse is #=((1,-1/a),(-1,2/a))#

The inverse of the matrix #A= ((x,y),(z,t))# is

#A^-1=1/detA*((t,-y),(-z,x))#

Here, we have

#A=((2,1),(a,a))# with #a!=0#

The determinant is

#detA=2a-a=a !=0#

As the #detA !=0#, the matrix is invertible

So,

#A^-1=1/a((a,-1),(-a,2))=((1,-1/a),(-1,2/a))#

Verification,

#A*A^-1=((2,1),(a,a))*((1,-1/a),(-1,2/a))=((1,0),(0,1))=I#