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Two matrics Aand B are said to anti — commute if
- a)AB = BA
- b)AB2 = A2B
- c)AB = -BA
- d)A/B = B/A
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Two matrics Aand B are said to anti — commute ifa)AB = BAb)AB2 =...
Explanation:
- Anti-commuting Property: For two matrices AAA and BBB, they are said to anti-commute if the product ABABAB is equal to the negative of the product BABABA. This means:AB=−BA
- Option Analysis:
- AB=BA: This defines matrices that commute, not anti-commute.
- AB^2=A^2B: This does not describe anti-commutation; it is a different property involving matrix powers.
- AB=−BA: This correctly describes anti-commutation.
- A/B=B/A: This is not a standard matrix operation and does not relate to anti-commutation.
Answer: AB=−BA
Most Upvoted Answer
Two matrics Aand B are said to anti — commute ifa)AB = BAb)AB2 =...
Two matrices A and B are said to be anti-symmetric if the transpose of matrix A is equal to the negative of matrix A, and the transpose of matrix B is equal to the negative of matrix B.
In mathematical notation, this can be expressed as:
A^T = -A
B^T = -B
In mathematical notation, this can be expressed as:
A^T = -A
B^T = -B
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Two matrics Aand B are said to anti — commute ifa)AB = BAb)AB2 =...
See...these options there is nothing difficult to understand
if you simplfy all the options you will easily get AB=BA that means A and B are commuting eachother but in "C" option
you will get anti-commutative case....so it's the correct ans
if you simplfy all the options you will easily get AB=BA that means A and B are commuting eachother but in "C" option
you will get anti-commutative case....so it's the correct ans
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