Let `I=((1,0,0),(0,1,0),(0,0,1)) and P=((1,0,0),(0,-1,0),(0,0,-2))`. Then the matrix `p^3+2P^2` is equal to

If A[(1, 0, 0),(x, 1, 0),(x, x, 1)] and I=[(1, 0, 0),(0,1,0),(0,0,1)] , then A^(3)-3A^(2)+3A is equal to

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

The matrix [(1,0,0),(0,2,0),(0,0,4)] is a

If P = [(d_(1),0,0),(0, d_(2),0),(0,0,d_(3))] then Adjoint (P) is equal to

The matrix |(1,0,0),(2,1,0),(3,1,1)| is

If {:A=[(1,2,x),(0,1,0),(0,0,1)]andB=[(1,-2,y),(0,1,0),(0,0,1)]:} and AB=I_3 , then x + y equals

(i) {:[( 1,0,0),( 0,1,0),( 0,0,1) ]:}" "(ii) {:[( 1,0,4),(3,5,-1),( 0,1,2) ]:}

Find the inverse of each of the matrices given below : Obtain the inverse of the matrics [(1,p,0),(0,1,p),(0,0,1)] and [(1,0,0),(q,1,0),(0,q,1)] . And, hence find the inverse of the matrix [((1+pq),p,0),(q,(1+pq),p),(0,q,1)] . Let the first two matrices be A and B. Then, the third matrix is AB. Now, (AB)^(-1)=(B^(-1)A^(-1))