If `A=[(2, 2),(9,4)]` and `A^(2)+aA+bI=O`. Then `a+2b` is equal to (where, I is an identity matrix and O is a null matrix of order 2 respectively)

Show that the matrix A=({:(2,-3),(3,4):}) satisfies the equation A^(2)-6A+17I=O and hence find A^(-1) where I is the identity matrix and O is the null matrix of order 2 times 2 .

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.

If A = ({:( 1,2,3),( 2,1,2),( 2,2,1) :}) and A^(2) -4A -5l =O where I and O are the unit matrix and the null matrix order 3 respectively if , 15A^(-1) =lambda |{:( -3,2,3),(2,-3,2),(2,2,-3):}| then the find the value of lambda

If A = ({:( 1,2,3),( 2,1,2),( 2,2,1) :}) and A^(2) -4A -5l =O where I and O are the unit matrix and the null matrix order 3 respectively if , 15A^(-1) =lambda |{:( -3,2,3),(2,-3,2),(2,2,-3):}| then the find the value of lambda

For a matrix A, if A^(2)=A and B=I-A then AB+BA +I-(I-A)^(2) is equal to (where, I is the identity matrix of the same order of matrix A)

For a matrix A, if A^(2)=A and B=I-A then AB+BA +I-(I-A)^(2) is equal to (where, I is the identity matrix of the same order of matrix A)

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)

If for a matrix A,A^(2)+I=O where I is the indentity matrix, then A=