If `A` is a skew symmetric matrix, then `B=(I-A)(I+A)^(-1)` is (where `I` is an identity matrix of same order as of `A`)

Question

If `A` is a skew symmetric matrix, then `B=(I-A)(I+A)^(-1)` is (where `I` is an identity matrix of same order as of `A`)

If `A` is a skew symmetric matrix, then `B=(I-A)(I+A)^(-1)` is (where `I` is an identity matrix of same order as of `A`)
A. idempotent matrix
B. symmetric matrix
C. orthogonal matrix
D. none of these

Monjur Alahi

6 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - C
`(c )` `B=(I-A)(I+A)^(-1)`
`impliesB^(T)=(I+A^(T))^(-1)(I-A^(T))`
`=(I-A)^(-1)(I+A)`
`impliesB B^(T)=(I-A)(I+A)^(-1)(I-A)^(-1)(I+A)`
`=(I-A)(I-A)^(-1)(I+A)^(-1)(I+A)`
`=I`
(As `(I-A).(I+A)=(I+A)(I-A)`)

6 views Answered 2023-02-05 15:29