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A and B are square matrices of order n x n, then (A - B)2 is equal to
a)A2 - 2AB + B2
b)A2 - B2
c)A2 - 2BA - B2
d)A2 - AB - BA + B2
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A and B are square matrices of order n x n, then (A - B)2 is equal toa...
(A - B) x (A - B)
(A - B) x A - (A - B) x B
= A2 - AB - BA + B2
(A - B) x A - (A - B) x B
= A2 - AB - BA + B2
Most Upvoted Answer
A and B are square matrices of order n x n, then (A - B)2 is equal toa...
(A - B) x (A - B)
(A - B) x A - (A - B) x B
= A2 - AB - BA + B2
(A - B) x A - (A - B) x B
= A2 - AB - BA + B2
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Community Answer
A and B are square matrices of order n x n, then (A - B)2 is equal toa...
Explanation:
Expansion of (A - B)^2:
- We start by expanding the square of the difference of two matrices (A - B) as follows:
- (A - B)^2 = (A - B)(A - B)
- = A(A - B) - B(A - B)
- = A^2 - AB - BA + B^2 (Expanding the terms using matrix multiplication rules)
Comparing with given options:
- Now, we compare our result with the options provided:
- Option a) A^2 - 2AB + B^2: This doesn't match our result as it has an extra term -2AB.
- Option b) A^2 - B^2: This doesn't match our result as it is missing the term -BA.
- Option c) A^2 - 2BA - B^2: This doesn't match our result as it has an extra term -2BA.
- Option d) A^2 - AB - BA + B^2: This matches our result exactly, so the correct answer is option d.
Therefore, after expanding (A - B)^2 and comparing it with the given options, we find that the correct answer is option d) A^2 - AB - BA + B^2.
Expansion of (A - B)^2:
- We start by expanding the square of the difference of two matrices (A - B) as follows:
- (A - B)^2 = (A - B)(A - B)
- = A(A - B) - B(A - B)
- = A^2 - AB - BA + B^2 (Expanding the terms using matrix multiplication rules)
Comparing with given options:
- Now, we compare our result with the options provided:
- Option a) A^2 - 2AB + B^2: This doesn't match our result as it has an extra term -2AB.
- Option b) A^2 - B^2: This doesn't match our result as it is missing the term -BA.
- Option c) A^2 - 2BA - B^2: This doesn't match our result as it has an extra term -2BA.
- Option d) A^2 - AB - BA + B^2: This matches our result exactly, so the correct answer is option d.
Therefore, after expanding (A - B)^2 and comparing it with the given options, we find that the correct answer is option d) A^2 - AB - BA + B^2.
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A and B are square matrices of order n x n, then (A - B)2 is equal toa)A2 - 2AB + B2b)A2 - B2c)A2 - 2BA - B2d)A2 - AB - BA + B2Correct answer is option 'D'. Can you explain this answer?
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