Question

Choose the correct answer in the following questions

If A = `[(alpha, beta),(y, - a)]` is such that A² = I, then

पर्याय

• 1 + α² + βy = 0

• 1 – α² + βy = 0

• 1 – α² – βy = 0

• 1 + α² – βy = 0

Answer 1

1 – α² – βy = 0

Explanation:

Given, A = `[(alpha, beta),(y, - alpha)]`

∴ A² = A, A = `[(alpha, beta),(y, -alpha)][(alpha, beta),(y, -alpha)]`

= `[(alpha^2 + betay, alphabeta - alphabeta),(alphay - alphay, betay + alpha^2)] = [(alpha^2 + betay, 0),(0, betay + alpha^2)]`

Now, A² = I

⇒ `[(alpha^2 + y, 0),(0, betay + alpha^2)] = [(1, 0),(0, 1)]`

We have equalting the corresponding elements.

`alpha^2 + betay` = 1

⇒ `alpha^2 + betay - 1` = 0

⇒ `1 - alpha^2 - betay` = 0