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If A and B are two matrices such that A+B and AB are both defined, then
- a)A and B can be any matrices
- b)A, B are square matrices not necessarily of the same order
- c)A, B are square matrices of the same order
- d)Number of columns of A = number of rows of B
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If A and B are two matrices such that A+B and AB are both defined, the...
Addition is defined if order of A is equal to order of B
A B
nxm nxm is defined if m = n
⇒ A, B are square matrices of same order
A B
nxm nxm is defined if m = n
⇒ A, B are square matrices of same order
Most Upvoted Answer
If A and B are two matrices such that A+B and AB are both defined, the...
Explanation:
When we multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix. The resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix.
To understand why option 'C' is the correct answer, let's break down the requirements for multiplying matrices:
1. A and B must be square matrices: A square matrix is one where the number of rows is equal to the number of columns. If A and B are not square matrices, then their product AB is not defined.
2. A and B must have the same order: The order of a matrix is the number of rows by the number of columns. If A and B do not have the same order, then their product AB is not defined.
3. The number of columns in A must equal the number of rows in B: This is the most important requirement for matrix multiplication. If the number of columns in A does not equal the number of rows in B, then their product AB is not defined.
So, if A and B are two matrices such that AB and BA are both defined, then the following must be true:
- A and B are square matrices of the same order
- The number of columns in A equals the number of rows in B
Therefore, option 'C' is the correct answer.
When we multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix. The resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix.
To understand why option 'C' is the correct answer, let's break down the requirements for multiplying matrices:
1. A and B must be square matrices: A square matrix is one where the number of rows is equal to the number of columns. If A and B are not square matrices, then their product AB is not defined.
2. A and B must have the same order: The order of a matrix is the number of rows by the number of columns. If A and B do not have the same order, then their product AB is not defined.
3. The number of columns in A must equal the number of rows in B: This is the most important requirement for matrix multiplication. If the number of columns in A does not equal the number of rows in B, then their product AB is not defined.
So, if A and B are two matrices such that AB and BA are both defined, then the following must be true:
- A and B are square matrices of the same order
- The number of columns in A equals the number of rows in B
Therefore, option 'C' is the correct answer.
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Community Answer
If A and B are two matrices such that A+B and AB are both defined, the...
A and B are of same order becoz they are adding
and both are square matrix as they both are adding and multiplying
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If A and B are two matrices such that A+B and AB are both defined, thena)A and B can be any matricesb)A, B are square matrices not necessarily of the same orderc)A, B are square matrices of the same orderd)Number of columns of A = number of rows of BCorrect answer is option 'C'. Can you explain this answer?
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If A and B are two matrices such that A+B and AB are both defined, thena)A and B can be any matricesb)A, B are square matrices not necessarily of the same orderc)A, B are square matrices of the same orderd)Number of columns of A = number of rows of BCorrect answer is option 'C'. Can you explain this answer? for 2024 is part of preparation. The Question and answers have been prepared according to the exam syllabus. Information about If A and B are two matrices such that A+B and AB are both defined, thena)A and B can be any matricesb)A, B are square matrices not necessarily of the same orderc)A, B are square matrices of the same orderd)Number of columns of A = number of rows of BCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A and B are two matrices such that A+B and AB are both defined, thena)A and B can be any matricesb)A, B are square matrices not necessarily of the same orderc)A, B are square matrices of the same orderd)Number of columns of A = number of rows of BCorrect answer is option 'C'. Can you explain this answer?.
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