If, for a 3 × 3 matrix A, AAT = I and |A| = 1, then |A - I| is equal to
Answer & explanation
Correct answer: option 3
We know that
|A - I| = |A - AAT|
= |A(I - AT)|
= |A| |(I - A)T|
= |I - A| = - |A - I|
⇒ |A - I| = 0.
If, for a 3 × 3 matrix A, AAT = I and |A| = 1, then |A - I| is equal to
Correct answer: option 3
We know that
|A - I| = |A - AAT|
= |A(I - AT)|
= |A| |(I - A)T|
= |I - A| = - |A - I|
⇒ |A - I| = 0.