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If A and B are any two matrices, then
- a)AB may or may not be defined.
- b)AB = O
- c)2A2
- d)A2 = O
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If A and B are any two matrices, thena)AB may or may not be defined.b)...
Let matrix A is of order m x n , and matrix B is of order p x q . then , the product AB is defined only when n = p. that’s why, If A and B are any two matrices, thenAB may or may not be defined.
Most Upvoted Answer
If A and B are any two matrices, thena)AB may or may not be defined.b)...
Explanation:
To understand why option A is the correct answer, we need to consider the properties of matrix multiplication.
Matrix Multiplication
When multiplying two matrices A and B, the number of columns in A must be equal to the number of rows in B. If this condition is not satisfied, then matrix multiplication is not defined.
Given that A and B are any two matrices, we cannot make any assumptions about their dimensions. Therefore, we cannot determine whether AB is defined or not without knowing the dimensions of A and B.
Option A: AB may or may not be defined
This option is correct because matrix multiplication is only defined when the dimensions of the matrices satisfy the condition mentioned above. Without knowing the dimensions of A and B, we cannot determine whether AB is defined or not. It is possible that AB is defined in some cases and not defined in others.
Option B: AB = O
This option is not always true. The zero matrix (O) is a matrix where all the elements are zero. It is possible for AB to be equal to O in some cases, but it is not a general result. The product of two matrices is not always the zero matrix.
Option C: 2A2
This option is not meaningful as it is not clear what is meant by "2A2". The notation "2A2" does not correspond to any valid matrix operation or expression.
Option D: A2 = O
This option is also not always true. The notation A2 typically represents the square of a matrix, which is obtained by multiplying the matrix by itself. It is possible for A2 to be equal to O in some cases, but it is not a general result. The square of a matrix is not always the zero matrix.
Therefore, the correct answer is option A. Without knowing the dimensions of A and B, we cannot determine whether AB is defined or not.
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If A and B are any two matrices, thena)AB may or may not be defined.b)AB = Oc)2A2d)A2 = OCorrect answer is option 'A'. 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 If A and B are any two matrices, thena)AB may or may not be defined.b)AB = Oc)2A2d)A2 = OCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A and B are any two matrices, thena)AB may or may not be defined.b)AB = Oc)2A2d)A2 = OCorrect answer is option 'A'. Can you explain this answer?.
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