A is a 2 x 2 matrix, I is 2 x 2 identity matrix. `IA - xIl=0` has the roots -1, 3. Then the sum of diagonal elements of `A^2`

Let A be a 2xx2 matrix with real entries. Let I be the 2xx2 identity matrix. Denote by tr (A), the sum of diagonal entries of A. Assume that A^2=""I . Statement 1: If A!=I and A!=""-I , then det A""=-1 . Statement 2: If A!=I and A!=""-I , then t r(A)!=0 .

Let "A" be a 2times2 real matrix and "I" be the identity matrix of order "2" .If the roots of the equation , [|A-xI|=0 be "-1" and "3" ,then the sum of the diagonal elements of the matrix A^(2) is______________

Let A be a 2 xx 2 real matrix with entries from { 0,1} and |A| ne 0 . Consider the following two statements : (P ) If A ne I_2 then |A| =-1 (Q ) if |A| =1 , then Tr (A)=2 Where I_2 denotes 2xx 2 identity matrix and tr (A) denotes the sum of the diagonal entries of A then :

Let A be a 2xx2 matrix with non-zero entries and let A^2=""I , where I is 2xx2 identity matrix. Define Tr(A) = sum of diagonal elements of A and |A| = determinant of matrix A. Statement-1: T r(A)""=""0 Statement-2: |A|""=""1 (1) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1 (2) Statement-1 is true, Statement-2 is false (3) Statement-1 is false, Statement-2 is true (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

Let A be a 2xx2 matrix with non zero entries and let A^(2)=I , where I is 2xx2 identity matrix. Define Tr(A)= sum of diagonal elemets of A and |A|= determinant of matrix A. Statement 1: Tr(A)=0 Statement 2: |A|=1 .

If is a 2 xx 2 identity matrix, then | (3I)^(30)|^(-1) =_____.

Let A be a 2xx2 matrix with non-zero entries and let A^(^^)2=I, where i is a 2xx2 identity matrix,Tr(A)i=sum of diagonal elements of A and |A|= determinant of matrix A.Statement 1:Tr(A)=0 Statement 2:|A|=1

The trace of a square matrix is defined to be the sum of its diagonal entries. If A is a 2times2 matrix such that the trace of A is 3 and the trace of A^(3) is -18 ,then the value of the determinant of A