Let A be a `2xx2`matrix with non-zero entriesand 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 istrue, Statement-2 is true; Statement-2 is not the correct explanation forStatement-1(2)Statement-1 istrue, Statement-2 is false(3)Statement-1 isfalse, Statement-2 is true(4)Statement-1 istrue, Statement-2 is true; Statement-2 is the correct explanation forStatement-1

Let A be a `2xx2`matrix with non-zero entriesand let `A^2=""I`, where

1.	Let A be a `2xx2`matrix with non-zero entriesand 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 istrue, Statement-2 is true; Statement-2 is not the correct explanation forStatement-1(2)Statement-1 istrue, Statement-2 is false(3)Statement-1 isfalse, Statement-2 is true(4)Statement-1 istrue, Statement-2 is true; Statement-2 is the correct explanation forStatement-1
Answer» `A= [(a,b),(c,d)]` `A^2 = [(a,b),(c,d)][(a,b),(c,d)] = [ (a^2 + bc,ab+bd),(ac+cd, bc+d^2)]= I` `I= [(1,0),(0,1)]` now,`a^2 + bc = bc+d^2 = 1` `ab + bd = ac + cd = 0` `b(a+d) = c(a+d) = 0` `a+d = 0` 1)`T_r = (A) = a+d = 0` 2) `det(A) = ad*bc = a(-a) - bc= -a^2 - bc` `= -(a^2 +bc)` option 2 is correct

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