Let `M` be a `3xx3` matrix satisfying `M[0 1 0]=M[1-1 0]=[1 1-1],a n dM[1 1 1]=[0 0 12]` Then the sum of the diagonal entries of `M` is _________.

Options

A. 7
B. 8
C. 9
D. 6

Answer

C

Explanation

Let `M={:[(a,b,c),(x,y,z),(l,m,n)]:}`. Then,
`{:M[(0),(1),(0)]=[(1),(-1),(6)]rArr [(b),(y),(m)]=[(-1),(2),(3)]rArr b=-1,y=2,m=3:}`
`{:M[(1),(-1),(0)]=[(1),(1),(1)]rArr a-b=1,x-y=1,l-m=-1:}`
`rArra=0,x=3,l=2`
and,
`{:M[(1),(1),(1)]=[(0),(0),(12)]rArra+b+c=0,x+y+z=0,l+m+n=12:}`
`rArr c=1,z=-1,n=7`
`:. " Sum of diagonal elements of "M=a+y+n=0+2+7=9`