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

Let A be a 2 xx 2 matrix with non-zero entries and let A^2=I, where i is a 2 xx 2 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

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 . (1) Statement 1 is false, Statement ( 2) (3)-2( 4) is true (6) Statement 1 is true, Statement ( 7) (8)-2( 9) (10) is true, Statement ( 11) (12)-2( 13) is a correct explanation for Statement 1 (15) Statement 1 is true, Statement ( 16) (17)-2( 18) (19) is true; Statement ( 20) (21)-2( 22) is not a correct explanation for Statement 1. (24) Statement 1 is true, Statement ( 25) (26)-2( 27) is false.

Let A be a 2xx 2 matrix with real entries and det (A)= 2 . Find the value of det ( Adj(adj(A) )

Let A be 2 x 2 matrix.Statement I adj (adj A) = A Statement II |adj A| = |A|

if for a matrix A, A^2+I=O , where I is the identity matrix, then A equals

Let M be a 2xx2 symmetric matrix with integer entries. Then , M is invertible, if

Let A be any 3xx2 matrix. Then prove that det. (A A^(T))=0 .

Let A be a 2xx2 matrix Statement -1 adj (adjA)=A Statement-2 abs(adjA) = abs(A)

Let A=[(0,1),(2,0)] and (A^(8)+A^(6)+A^(2)+I)V=[(32),(62)] where I is the (2xx2 identity matrix). Then the product of all elements of matrix V is

Let A be any 3xx 2 matrix show that AA is a singular matrix.