Let A = a b c d and B = α β ≠ 0 0 such that A B = B and a + d =2021, then the value of a d -…

Let A=abcd and B=αβ≠00 such that AB=B and a+d=2021, then the value of ad-bc is equal to ______ .

Solution

Given A=abcd, B=αβ

And, AB=B

⇒(A-I)B=O

⇒(A-I)B=0

⇒(A-I)×B=0

⇒|A-I|=0, since B≠0

⇒(a-1)bc(d-1)=0

⇒a-1d-1-bc=0

⇒ad-a-d+1-bc=0

⇒ad-bc=a+d-1

⇒ad-bc=2021-1=2020.

Asked in: JEE Main 2021 (17 Mar Shift 2)

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