Question

Choose the correct answer from the given four options :

If A = `[(2, -2),(-2, 2)]`, then A² = pA, then the value of p is

Options

• 2

• 4

• – 2

• – 4

Answer 1

A = `[(2, -2),(-2, 2)]`
and A² = pA

A² = A x A = `[(2, -2),(-2, 2)] xx [(2, -2),(-2, 2)]`

= `[(4 + 4, -4 - 4),(-4 - 4, 4 + 4)]`

= `[(8, -8),(-8, 8)]`

pA = `"p"[(2, -2),(-2, 2)]`

= `[(2"p", -2"p"),(-2"p", 2"p")]`
∵ A² = pA
∴ `[(8, -8),(8, 8)] = [(2"p", -2"p"),(-2"p", 2"p")]`
Comparing, we get
8 = 2p
⇒ p = 4.