If `A=({:(5,8),(8,13):})`, show that the matrix equation `x^(2)-18x+1=0` is satisfied by both the matrices A and `A^(_1)` (I is the identity matrix of order two).

The equation 8x^3-6x+sqrt3=0 is satisfied by

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 = [[2,2],[4,3]] show that A A^(-1) = I_2 where I_2 is the unit matrix of order 2.

If A is a skew symmetric matrix, then B=(I-A)(I+A)^(-1) is (where I is an identity matrix of same order as of A )

If A = [(2,2),(4,3)] show that, A A^(-1) =I_(2) wher I_(2) is the unit matrix of order 2.

Two roots of the quadratic equation x^(2) +(i -5)x +18 +i =0 are -

If 2X+[(1,2),(3,4)]=[(3,8),(7,2)] , then the matrix X is equal to -

If A = [(4,1),(7,2)] find a matrix B such that AB = I where I is the unit matrix of order 2.

If A be a 2 times 2 matrix such that A^(2)=A , then show that (I-A)^(2)=I-A where I is the unit matrix of order 2 times 2 .

Verify that the matrix equation A^2 - 4a +3I =0 is satisfied by the matrix A = [[2,-1],[-1,2]] , where I = [[1,0],[0,1]] and 0= [[0,0],[0,0]] ,