Question

If A = `[(cos a, - sin a),(sin a, cos a)]`, then A+ A¹ = l, if the value of a is:

Options

• `pi/6`

• `pi/3`

• `n`

• `(3pi)/2`

Answer 1

`pi/3`

Explanation:

A = `[(cos a, - sin a),(sin a, cos a)]`

⇒ `[(cos a, sin a),(- sin a, cos a)]`

Now A + A = 1

`[(cos a, - sin a),(sin a, cos a)] + [(cos a, sin a),(-sin a, cos a)] = [(1, 0),(0, 1)]`

⇒ `[(2cosa, 0),(0, 2cosa)] = [(1, 0),(0, 1)]`

Equating the corresponding elements of the two matrices, we have

`cos a = 1/2`

`a = cos^-1 (1/2) = pi/3`