For the matrix `A=|(1,1,1),(1,2,-3),(2,-1,3)|,` then that `A^3-6A^2+5A+11I=0.` find `A^-1`

For the matrix A=det[[1,1,11,2,-32,-1,3]], then that A^(3)-6A^(2)+5A+4I=0., find A^(-1)

For the matrix A=[11112-32-13]. Show that A^(3)-6A^(2)+5A+11I_(3)=O. Hence find A^(-1) .

If A= [(1,1,3),(5,2,6),(-2,-1,-3)] then find A^(14)+3A-2I

For the matrix A=[[1,1,11,2,-32,1,3]]*A^(3)-6A^(2)+5A+11I=0. Hence,find

For the matrix A=[{:(,3,2),(,1,1):}] Find a & b so that A^(2)+aA+bI=0 . Hence find A^(-1)

if A[{:(1,3,2),(2,0,3),(1,-1,1):}], then find A^(3)-2A^(2)+A-I_(3).

Find matrix A.A+I_(3)=[[1,3,4-1,1,3-2,-3,1]]

Evaluate |{:(1,2,3),(3,-1,1),(2,3,5):}|

Show that the matrix [{:( 1,1,3),( 5,2,6),( -2,-1,-3):}] is nilpotent matrix of index 3.

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