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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
Solution
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.
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