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IF A is a skew syemmetric matrix, then B=(I-A)(I+A) -1 is (here I is the identity matrix of the same order as A) 1)idempotent matrix 2)syemmetric matrix 3)orthogonal matrix 4)None

IF A is a skew syemmetric matrix, then B=(I-A)(I+A)-1 is (here I is the identity matrix of the same order as A)
1)idempotent matrix
2)syemmetric matrix
3)orthogonal matrix
4)None

Grade:12th pass

2 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
5 years ago
Lets take
B^T = ((I+A)^T)^{-1}(I-A)^T = (I-A)^{-1}(I+A)
this is because A is skew symmetric
Now lets do
B^TB = ((I+A)^T)^{-1}(I-A)^T = (I-A)^{-1}(I+A)(I-A)(I+A)^{-1}and
(I-A)(I+A) = (I+A)(I-A) ….... try this, putting in the above equation we get
BTB = I
Hence orthogonal
Madhab Pal Choudhury
25 Points
5 years ago
this is because AT=-A in case of skew syemmetric matrix right so why the first line is that very good

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