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Let M and N be two 3 x 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
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?
Most Upvoted Answer
Let M and N be two 3 x 3 non-singular skew symmetric matrices such tha...
Using the property of transpose, we have:
(MN)T = NTMT
Since MN = NM, we can rewrite the above equation as:
MTNT = NTMT
Multiplying both sides by N on the left, we get:
NTMTN = NTMTN
Since N is non-singular, we can cancel it from both sides to get:
MTN = NTN
Now, let's evaluate M2N2(MTN):
M2N2(MTN) = M2N2(NTMT)
Using the commutative property of matrix multiplication, we can rearrange the order of multiplication:
M2N2(NTMT) = M2(NTMT)N2
Since M and N are skew symmetric matrices, we have:
M2 = -M and N2 = -N
Substituting these values, we get:
M2N2(NTMT) = -M(NTMT)(-N)
Multiplying the matrices, we have:
M2N2(NTMT) = MN(NTMT)N
Since MN = NM, we can write it as:
M2N2(NTMT) = NM(NTMT)N
Using the associativity property of matrix multiplication, we can rearrange the order of multiplication:
M2N2(NTMT) = N(MNT)(NT)N
Using the fact that MNT = MTN, we have:
M2N2(NTMT) = N(MTN)(NT)N
Since MTN = NTN, we can rewrite it as:
M2N2(NTMT) = N(NTMT)(NT)N
Using the fact that (NT)T = N, we have:
M2N2(NTMT) = N(NTMT)NN
Since NN = N2 = -N, we can substitute it in:
M2N2(NTMT) = N(NTMT)(-N)
Multiplying the matrices, we have:
M2N2(NTMT) = NTMTNTN
Using the fact that NTNT = -N2 = N, we have:
M2N2(NTMT) = NTMTNN
Since NN = N2 = -N, we can substitute it in:
M2N2(NTMT) = NTMT(-N)
Multiplying the matrices, we have:
M2N2(NTMT) = -NTMTN
Since NTMTN = -M2N2(MTN), we can substitute it in:
M2N2(NTMT) = -(-M2N2(MTN))
Simplifying the double negative, we get:
M2N2(NTMT) = M2N2(MTN)
Therefore, M2N2(NTMT) is equal to M2N2(MTN).
(MN)T = NTMT
Since MN = NM, we can rewrite the above equation as:
MTNT = NTMT
Multiplying both sides by N on the left, we get:
NTMTN = NTMTN
Since N is non-singular, we can cancel it from both sides to get:
MTN = NTN
Now, let's evaluate M2N2(MTN):
M2N2(MTN) = M2N2(NTMT)
Using the commutative property of matrix multiplication, we can rearrange the order of multiplication:
M2N2(NTMT) = M2(NTMT)N2
Since M and N are skew symmetric matrices, we have:
M2 = -M and N2 = -N
Substituting these values, we get:
M2N2(NTMT) = -M(NTMT)(-N)
Multiplying the matrices, we have:
M2N2(NTMT) = MN(NTMT)N
Since MN = NM, we can write it as:
M2N2(NTMT) = NM(NTMT)N
Using the associativity property of matrix multiplication, we can rearrange the order of multiplication:
M2N2(NTMT) = N(MNT)(NT)N
Using the fact that MNT = MTN, we have:
M2N2(NTMT) = N(MTN)(NT)N
Since MTN = NTN, we can rewrite it as:
M2N2(NTMT) = N(NTMT)(NT)N
Using the fact that (NT)T = N, we have:
M2N2(NTMT) = N(NTMT)NN
Since NN = N2 = -N, we can substitute it in:
M2N2(NTMT) = N(NTMT)(-N)
Multiplying the matrices, we have:
M2N2(NTMT) = NTMTNTN
Using the fact that NTNT = -N2 = N, we have:
M2N2(NTMT) = NTMTNN
Since NN = N2 = -N, we can substitute it in:
M2N2(NTMT) = NTMT(-N)
Multiplying the matrices, we have:
M2N2(NTMT) = -NTMTN
Since NTMTN = -M2N2(MTN), we can substitute it in:
M2N2(NTMT) = -(-M2N2(MTN))
Simplifying the double negative, we get:
M2N2(NTMT) = M2N2(MTN)
Therefore, M2N2(NTMT) is equal to M2N2(MTN).
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Let M and N be two 3 x 3 non-singular skew symmetric matrices such tha...
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Let M and N be two 3 x 3 non-singular skew symmetric matrices such that MN = NM. If PT denotes thetranspose 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 x 3 non-singular skew symmetric matrices such that MN = NM. If PT denotes thetranspose 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 x 3 non-singular skew symmetric matrices such that MN = NM. If PT denotes thetranspose 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 x 3 non-singular skew symmetric matrices such that MN = NM. If PT denotes thetranspose 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 x 3 non-singular skew symmetric matrices such that MN = NM. If PT denotes thetranspose 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 x 3 non-singular skew symmetric matrices such that MN = NM. If PT denotes thetranspose 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 x 3 non-singular skew symmetric matrices such that MN = NM. If PT denotes thetranspose 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 x 3 non-singular skew symmetric matrices such that MN = NM. If PT denotes thetranspose 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?, a detailed solution for Let M and N be two 3 x 3 non-singular skew symmetric matrices such that MN = NM. If PT denotes thetranspose 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? has been provided alongside types of Let M and N be two 3 x 3 non-singular skew symmetric matrices such that MN = NM. If PT denotes thetranspose 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? theory, EduRev gives you an
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