Question

If A = `[(x,1),(1,0)]` and A = A , then x = ______.

Options

• 0

• 4

• 2

• 1

Answer 1

If A = `[(x,1),(1,0)]` and A = A , then x = 0.

Explanation:

We have, A = `[(x,1),(1,0)]`

∴ |A| = `(x × 0 - 1) = - 1`

adj A = `[(0,-1),(-1,x)]`

`"A"^-1 = ("adj A")/|"A"|`

`= (- 1) [(0,-1),(-1,x)]`

`= [(0,1),(1,-x)]`

Since, It is given, A = A^-1

`=> [(x,1),(1,0)] = [(0,1),(1,-x)]`

⇒ x = 0    (By equality of matrices)