If A `=[{:(0,1,0),(0,0,1),(p,q,r):}]`, show that ltbargt `A^(3)= pI+qA+rA^(2)`

If a matrix A=((3,2,0),(1,4,0),(0,0,5)) show that A^2-7A+10I_(3) = 0 and hence find A^(-1)

If A=[(1,1),(0,1)] , show that A^2=[(1, 2),( 0, 1)] and A^3=[(1 ,3 ),(0 ,1)] .

If P=[(lambda,0),(7,1)] and Q=[(4,0),(-7,1)] such that P^(2)=Q , then P^(3) is equal to

If A=[[1 ,0 ,1],[0 ,1, 2],[ 0, 0, 4]] , then show that |3A| = 27|A|

If A=[[1 ,0 ,1],[0 ,1, 2],[ 0, 0, 4]] , then show that |3A|" "=" "27|A|

If A=((p,q),(0,1)) , then show that A^(8)=((p^(8),q((p^(8)-1)/(p-1))),(0,1))

Point P(p ,0),Q(q ,0),R(0, p),S(0,q) from.

Let P=[(1,2,1),(0,1,-1),(3,1,1)] . If the product PQ has inverse R=[(-1,0,1),(1,1,3),(2,0,2)] then Q^(-1) equals

If (a + (1)/(a))^(2) = 3 and a ne 0 , then show that: a^(3) + (1)/(a^(3))= 0

Let the matrices A=[{:( sqrt3,-2),(0,1):}] and P be any orthogonal matrix such that Q = PAP' and let Rne [r_0] _(2-2)=P'Q^(6) P then