If `A=(1)/(3){:[(-1,2,-2),(-2,1,2),(2,2,1)]` show that `"AA"^(T)=I`.

Show that A=(1)/(3)[{:(-1,2,-2),(-2,1,2),(2,2,1):}] is proper orthogonal matrix.

If A=[(1,2,3),(3,-2,1),(4,2,1)] , then show that A^(3)-23A-40I=0

Show that , A^(-1) = (1)/(3) [(-1,2,-2),(-2,1,-2),(2,2,1)] is a proper orthogonal matrix.

If P={:[(2,-2,-4),(-1,3,4),(1,-2,-3)]:} then show that, p^(2)=p .

Show that the matrix A = (1)/(3)[(1,2,2),(2,1,-2),(-2,2,-1)] is orthogonal, Hence, find A^(-1) .

If A={:[(1,2,5),(-1,3,-4)]:} and B={:[(3,-2,1),(0,-1,4),(5,2,-1)]:}, show that, (AB)^(T)=B^(T)A^(T) where A^(T) is the transpose of A.

If the matrix A=1/3 {:((a,2,2),(2,1,b),(2,c,1)):} obeys the law "AA"'=I, find a,b,and c (Here A' is the transpose of A and I is the unit matrix of order 3).

If A=[(3,1),(-1,2)] , show that A^(2)-5A+7I=0 .

Show that, the matrix A = [(1,2,2),(2,1,2),(2,2,1)] satisfies the equation A^(2) - 4A - 5I_(3) = 0 and hence find A^(-1) .

If A=[(1,2,3),(2,1,2),(2,2,3)]B=[(1,2,2),(-2,-1,-2),(2,2,3)] and C=[(-1,-2,-2),(2,1,2),(2,2,3)] then find the value of tr. (A+B^(T)+3C) .