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Let M and N be two 3 × 3 non-singular skew- symmetric matrices such that MN = NM. If PT denotes the transpose of P, then M2N2 (MTN)–1 (MN–1)T is equal to
- a)M2
- b)– N2
- c)– M2
- d)MN
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Let M and N be two 3 × 3 non-singular skew- symmetric matrices s...
[As a skew symmetric matrix of order 3 cannot be non singular, therefore the data given in the question is inconsistent.]
We have M2N2 (MT N)–1 (MN–1)T = M2N2N–1 (MT)–1 (N–1)T
MT
= M2 N (MT)–1 (N–1)T MT = –M2NM–1 N–1M
(∵ MT = –M, NT = –N and (N–1)T = (NT)–1
= – M (NM) (NM)–1 M (∵ MN = NM)
= – MM = –M2
We have M2N2 (MT N)–1 (MN–1)T = M2N2N–1 (MT)–1 (N–1)T
MT
= M2 N (MT)–1 (N–1)T MT = –M2NM–1 N–1M
(∵ MT = –M, NT = –N and (N–1)T = (NT)–1
= – M (NM) (NM)–1 M (∵ MN = NM)
= – MM = –M2
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Let M and N be two 3 × 3 non-singular skew- symmetric matrices such that MN = NM. If PT denotes the transpose of P, then M2N2 (MTN)–1 (MN–1)T is equal toa)M2b)– N2c)– M2d)MNCorrect answer is option 'C'. Can you explain this answer?
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Let M and N be two 3 × 3 non-singular skew- symmetric matrices such that MN = NM. If PT denotes the transpose of P, then M2N2 (MTN)–1 (MN–1)T is equal toa)M2b)– N2c)– M2d)MNCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let M and N be two 3 × 3 non-singular skew- symmetric matrices such that MN = NM. If PT denotes the transpose of P, then M2N2 (MTN)–1 (MN–1)T is equal toa)M2b)– N2c)– M2d)MNCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let M and N be two 3 × 3 non-singular skew- symmetric matrices such that MN = NM. If PT denotes the transpose of P, then M2N2 (MTN)–1 (MN–1)T is equal toa)M2b)– N2c)– M2d)MNCorrect answer is option 'C'. Can you explain this answer?.
Let M and N be two 3 × 3 non-singular skew- symmetric matrices such that MN = NM. If PT denotes the transpose of P, then M2N2 (MTN)–1 (MN–1)T is equal toa)M2b)– N2c)– M2d)MNCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let M and N be two 3 × 3 non-singular skew- symmetric matrices such that MN = NM. If PT denotes the transpose of P, then M2N2 (MTN)–1 (MN–1)T is equal toa)M2b)– N2c)– M2d)MNCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let M and N be two 3 × 3 non-singular skew- symmetric matrices such that MN = NM. If PT denotes the transpose of P, then M2N2 (MTN)–1 (MN–1)T is equal toa)M2b)– N2c)– M2d)MNCorrect answer is option 'C'. Can you explain this answer?.
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