What is the correct option?

sample paper nest-junior

2 Answers

Answer:

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

Explanation:

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

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

Jul 28, 2018

Answer:

The answer is #option (D)#

Explanation:

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)#