Show that the matrix `A=[(5, 3), (12 ,7)]` then show `A^2-12 A-I=O` .

Show that the matrix A=[(2, 3), (1, 2)] satisfies the equation A^3-4A^2+A=O .

Show that the matrix A=[2 3 1 2] satisfies the equation A^2-4A+I=0

If A=[(1,2),(2,1)] show that A^(2)-3I=2A

Show that thematrix A= [{:(,2,3),(,1,2):}] satisfies the equations A^(2)-4A+I=0 where I is 2 xx 2 identity matrix and O is 2 xx 2 zero matrix. Using the equations. Find A^(-1) .

show that the matrix A=[(-5,-8,0),(3,5,0),(1,2,-1)] is involutory.

The adjoint of the matrix A= [{:( 1,2),( 3,-5) :}] is

(i) Show that the matrix A=[{:(1,-1,5),(-1,2,1),(5,1,3):}] is a symmetric matrix. (ii) Show that the matrix A-[{:(0 ,1,-1),(-1, 2, 1),( 1,-1, 0):}] is a skew symmetric matrix.

(i) Show that the matrix A=[[1,-1, 5],[-1, 2, 1],[ 5, 1, 3]] is a symmetric matrix. (ii) Show that the matrix A=[[0, 1,-1],[-1, 2, 1],[ 1,-1, 0]] is a skew symmetric matrix.

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

Show that A=[(6, 5),( 7, 6)] satisfies the equation x^2-12 x+1=0 . Thus, find A^(-1)