Given A

Transpose of a matrix: If A be an m×n matrix, then the matrix obtained by interchanging the rows and columns of A is called the transpose of A. It is denoted by A’ or A^T.

∴ Transpose of A = A’ =

Given equation

A’A =I

=

=

. =

As these matrices are equal to each other that means each element of matrix on L.H.S is equal each element of matrix on R.H.S.

∴ On comparing elements on both sides we get

4y² + z² = 1 …… (1)

2y² – z² = 0 …… (2)

x² + y² + z² = 1 …… (3)

– y² – z² = 0 …… (4)

From equation (4) we get,

x² = y² + z² …… (5)

Substituting this value in equation (3) we get,

2y² + 2z² = 1 …… (6)

Subtracting equation (2) and (6) we get,

3z² = 1

z² = 1/3

z = 1/3

Substituting value of z in equation (2) we get,

2y² = 1/3

y² = 1/6

y = �1/6

Substituting values of y and z in equation (5) we get,

x² = 1/2

x = �1/2

Hence values of x, y, z are �1/2, �1/6, �1/3 respectively.