DeterminantHard
Question
If A is a square matrix of order 3 and A′ denotes transpose of matrix A, A′ A = I and det A = 1, then
det (A - I) must be equal to
det (A - I) must be equal to
Options
A.0
B.-1
C.1
D.none of these
Solution
A′A = I
|A - I | = |A - A′A|
⇒ |A - I| = |A| |I - A′|
⇒ |A - I| = - 1 . |A′ - I|
⇒ |A - I| = - |A - I|
⇒ |A - I| = 0
|A - I | = |A - A′A|
⇒ |A - I| = |A| |I - A′|
⇒ |A - I| = - 1 . |A′ - I|
⇒ |A - I| = - |A - I|
⇒ |A - I| = 0
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