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Show that A=[2-3 3 4] satisfies the equa...

Show that `A=[2-3 3 4]` satisfies the equation `x^2-6x+17=0` . Hence, find `A^(-1)` .

Text Solution

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Given,`A=[[2,-3],[ 3 ,4]]`
`A^2=A.A=[[2,-3],[ 3 ,4]].[[2,-3],[ 3 ,4]]=[[-5,-18],[ 18 ,7]]`
`6A=[[12,-18],[ 18 ,24]]`
Thus,`A^2−6A+17I=​[[-5,-18],[ 18 ,7]]-[[12,-18],[ 18 ,24]]+[[17,0],[ 0,17]]`
=`[[0,0],[ 0,0]]`
Hence, matrix A satisfies the equation, `x^2−6x+17=0`
Now , `A^2−6A+17I​=0⇒A^2−6A=−17I`
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