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 _________.

Answer

9

Explanation

Let `M=[(a,b,c),(d,e,f),(g,h,i)]`
`M[(0),(1),(0)]=[(-1),(2),(3)] implies b=-1, e=2, h=3`
`M[(1),(-1),(0)]=[(1),(1),(-1)]implies a=0, d=3, g=2`
`M[(1),(1),(1)]=[(0),(0),(12)]=g+h+i=12 implies i=7`
Therefore, sum of diagonal elements=9.