If the matrix `A=[[5,3],[12,7]]`, then verify that `A^2-12-I=O` where I is a unit matrix.

If A= [[ 3,-5,],[-4,2,]] ,show that A^2-5A-14I=O, where I is a unit matrix of Oder 2.

If A=[[3,1],[-1,2]] prove that A^2-5A+7I=O ,where I is unit matrix of order 2.

Show that the matrix A=[[2,3,],[1,2,]] satisfies the equation A^2-4A+I=O where I is a 2xx2 identity matrix and O is 2xx2 zero matrix.Using this equation.find A^-1 .

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

If A=[[5,2],[7,3]] ,then verify that A.adj A=|A|I, where I is the identity matrix of order

If A=[[1,0],[-1,7]] find k so that A^2-8A-kI=O ,where I is a unit matrix and O is a null matrix of oreder 2.

Show that the matrix A = [[2,3],[1,2] satisfies the equation A^2-4A+I = O , where I is 2xx2 identity matrix and O is, 2xx2 zero matrix. Using this equation, find A^-1 .

For the matrix A=[[1, 5],[ 6, 7]] , verify that.(i) (A+A^(prime)) is a symmetric matrix(ii) (A-A^(prime)) is a skew symmetric matrix

For the matrix A=[[1, 5],[ 6, 7]] , verify that.(i) (A+A^(prime)) is a symmetric matrix(ii) (A-A^(prime)) is a skew symmetric matrix