Let M be a `3xx3` matrix satisfying
`M[(0),(1),(0)]=[(-1),(2),(3)], M[(1),(-1),(0)]=[(1),(1),(-1)]`, and `M[(1),(1),(1)]=[(0),(0),(12)]`
Then the sum of the diagonal entries of M is ____.

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 _________.

Let a be a 3xx3 matric such that [(1,2,3),(0,2,3),(0,1,1)]=[(0,0,1),(1,0,0),(0,1,0)] , then find A^(-1) .

The matrix A satisfying the equation [(1,3),(0,1)] A= [(1,1),(0,-1)] is

Let A=[(1,2,3),(2,0,5),(0,2,1)] and B=[(0),(-3),(1)] . Which of the following is true ?

The matrix is [(4,3,1),(0,2,3),(0,0,-2)] is:

Let A be any 3xx2 matrix. Then prove that det. (A A^(T))=0 .

Let A=[(1,0,0),(1,0,1),(0,1,0)] satisfies A^(n)=A^(n-1)+A^(2)-I for n ge 3 . And trace of a square matrix X is equal to the sum of elements in its proncipal diagonal. Further consider a matrix underset(3xx3)(uu) with its column as uu_(1), uu_(2), uu_(3) such that A^(50) uu_(1)=[(1),(25),(25)], A^(50) uu_(2)=[(0),(1),(0)], A^(50) uu_(3)=[(0),(0),(1)] Then answer the following question : The values of |A^(50| equals

Let A=[(1,0,0),(1,0,1),(0,1,0)] satisfies A^(n)=A^(n-1)+A^(2)-I for n ge 3 . And trace of a square matrix X is equal to the sum of elements in its proncipal diagonal. Further consider a matrix underset(3xx3)(uu) with its column as uu_(1), uu_(2), uu_(3) such that A^(50) uu_(1)=[(1),(25),(25)], A^(50) uu_(2)=[(0),(1),(0)], A^(50) uu_(3)=[(0),(0),(1)] Then answer the following question : Trace of A^(50) equals

If A=[{:(3,-3,4),(2,-3,4),(0,-1,1):}] , then the trace of the matrix Adj(AdjA) is