If `A^2+A+I=0` , then A is non-singular `A!=0` (b) A is singular `A^(-1)=-(A+I)`

If A, B are two n xx n non-singular matrices, then (1) AB is non-singular (2) AB is singular (3) (AB)^(-1)=A^(-1) B^(-1) (4) (AB)^(-1) does not exist

If A is a non - singular matrix then

If A is a matrix such that A^2+A+2I=Odot, the which of the following is/are true? (a) A is non-singular (b) A is symmetric (c) A cannot be skew-symmetric (d) A^(-1)=-1/2(A+I)

If A is a non-singular matrix, prove that: adjA is also non -singular (adjA)^-1=1/|A| A .

If A is a non-singular square matrix such that |A|=10 , find |A^(-1)|

(Statement1 Assertion and Statement- 2 (Reason) Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice as given below. Statement - 1 If matrix A= [a_(ij)] _(3xx3) , B= [b_(ij)] _(3xx3), where a_(ij) + a_(ji) = 0 and b_(ij) - b_(ji) = 0 then A^(4) B^(5) is non-singular matrix. Statement-2 If A is non-singular matrix, then abs(A) ne 0 .

If A is a non-singular matrix of order nxxn such that 3ABA^(-1)+A=2A^(-1)BA , then

If A is a non-singular matrix, prove that: a d j\ (A) is also non-singular (ii) (a d j\ A)^(-1)=1/(|A|)Adot

A square non-singular matrix A satisfies A^2-A+2I=0," then "A^(-1) =

If A ,\ B are square matrices of order 3,\ A is non-singular and A B=O , then B is a (a) null matrix (b) singular matrix (c) unit matrix (d) non-singular matrix