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Question

If for the matrix, A=1-ααβ AAT=I2, then the value of α4+β4 is:


A

1

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B

3

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C

2

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D

4

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Solution

The correct option is A

1


Explanation for the correct option:

Step 1. Find the value of α4+β4:

Given, A=1-ααβ

then, AT=1α-αβ

AAT=1-ααβ1α-αβ=1+α2α-αβα-αβα2+β2GivenThat,AAT=I21+α2α-αβα-αβα2+β2=1001

Step 2. Compare the corresponding values with identity matrix:

1+α2=1

α2=0

α2+β2=1

β2=1

α4=0 and β4=1

Thus, α4+β4=1

Hence, Option ‘A’ is Correct.


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