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

If A=[[1,0,-32,1,30,1,1]], then verify that A^(2)+A=A(A+I), where I is the identity matrix.

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

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

If A=[[4,32,5]], find values of x and y such that A^(2)-xA+yI=O where I is a 2x2 unit matrix and O is a 2x2 zero matrix.

For the matrix A=[[1,5,-1],[6,7,2],[0,1,3]] verify that: (i) A+A^(T) is a Symmetric matrix. ii. A-A^(T) is a skew symmetric matrix.

Show that the matrix A=[[5,312,7]] is a root of the equation A^(2)-12A-I=O

If A=[122212221], then show that A^(2)-4A-5I=O, where Iand 0 are the unit matrix and the null matrix of order 3, respectively.Use this result to find A^(-1)

for the matrix A=[{:(1,5),(6,7):}], verify that : (I) (A+A') is a symmetric matrix. (ii) (A-A') is a skew symmetric matrix.

[" A skew - symmetric matrix "S],[" satisfies the relation "S^(2)+I=0],[" where "|" is a unit matrix then "S" is "]