What is the correct option?

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Answer 1 · 2018-07-28T04:35:00

Option (D) #9I-A# is correct

Find #A^{-1}=\frac{\adj(A)}{|A|}#

Check the options. Option (D) satisfies the given condition

Answer 2 · 2018-07-28T05:58:51

The answer is #option (D)#

The matrix is

#A=((2,-3),(-4,7))#

The inverse of a matrix

#A=((a,b),(c,d))# is

#A^-1=1/(det A)((d,-b),(-c,a))#

The determinant of

#|A|=ad-bc=2*7-(-3*-4)=14-12=2#

Therefore,

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

And

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

#9I-A=9((1,0),(0,1))-((2,-3),(-4,7))#

#=((7,3),(4,2))#

#=2A^-1#

The answer is #option (D)#