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Grade 12th passAlgebra

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

Madhab Pal Choudhury

10 Years agoGrade 12th pass

2 Answers

Riddhish Bhalodia

Approved Tutor Answer10 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
B^TB = I
Hence orthogonal

Madhab Pal Choudhury

10 Years ago

this is because A^T=-A in case of skew syemmetric matrix right so why the first line is that very good

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