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If A=[[a+i b, c+i d],[-c+i d, a-i b]] an...

If `A=[[a+i b, c+i d],[-c+i d, a-i b]] and a^2+b^2+c^2+d^2=1,t h e n ,A^(-1)` is equal to a.`[[a+i b,-c+i d],[c+i d, a-i b]]` b. `[[a-i b,-c-i d],[-c-i d, a+i b]]` c. `[[a+i b,-c-i d],[-c+i d, a-i b]]` d. none of these

A

`[(a-ib,-c-id),(c-id,a+ib)]`

B

`[(a+ib,-c+id),(-c+id,a-ib)]`

C

`[(a-ib,-c-id),(-c-id,a+ib)]`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`|A|=(a+ib) (a-ib)-(-c+id) (c+id)`
`=a^(2)+b^(2)+c^(2)+d^(2)=1`
and adj `(A)=[(a-ib,-c-id),(c-id,a+ib)]`
Then `A^(-1)=[(a-ib,-c-id),(c-id,a+ib)]`
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