If `P={:[(-1,3,5),(1,-3,-5),(-1,3,5)],` show that, `P^(2)=P` hence find matrix Q such that `3P^(2)-2P+Q=I`, where I is the unit matrix of order 3.

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

If A = [[2,2],[4,3]] show that A A^(-1) = I_2 where I_2 is the unit matrix of order 2.

If A = [(2,2),(4,3)] show that, A A^(-1) =I_(2) wher I_(2) is the unit matrix of order 2.

If P=[{:(2,-2,-4),(-1,3,4),(1,-2,-3):}] , then P^(5) equals-

Let A=[("tan"pi/3,"sec" (2pi)/3),(cot (2013 pi/3),cos (2012 pi))] and P be a 2 xx 2 matrix such that P P^(T)=I , where I is an identity matrix of order 2. If Q=PAP^(T) and R=[r_("ij")]_(2xx2)=P^(T) Q^(8) P , then find r_(11) .

If for a matrix A, A= A^(-1) , then show that A(A^(3)+I)=A+I (I is the unit matrix).

A square matrix P satisfies P^(2)=I-P , where I is identity matrix. If P^(n)=5I-8P , then n is :

If A = [(4,5),(5,6)] show that, A^(2) = 10A + I where I is the unit matrix or order 2. Hence, find the inverse of A.

If A={:((3,2),(3,3))and B={:((1,-2/3),(-1,1)) show that AB=I_(2) where I_(2) is the unit matrix of order 2.

Show that the matrix A=({:(2,-3),(3,4):}) satisfies the equation A^(2)-6A+17I=O and hence find A^(-1) where I is the identity matrix and O is the null matrix of order 2 times 2 .