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

Explanation

`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`

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