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Consider the following statements:
1. The product of two non-zero matrices can never be identity matrix.
2. The product of two non-zero matrices can never be zero matrix.
Q. Which of the above statements is/are correct ?
- a)1 only
- b)2 only
- c)Both 1 and 2
- d)Neither 1 nor 2
Correct answer is option 'D'. Can you explain this answer?
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Consider the following statements:1. The product of two non-zero matri...
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Consider the following statements:1. The product of two non-zero matri...
Explanation:
1. Product of two non-zero matrices can never be identity matrix:
- This statement is incorrect. The product of two non-zero matrices can result in an identity matrix under certain conditions. For example, if matrix A is invertible and matrix B is its inverse, then the product AB will result in an identity matrix.
2. Product of two non-zero matrices can never be zero matrix:
- This statement is also incorrect. The product of two non-zero matrices can result in a zero matrix. For example, consider two 2x2 matrices A = [1 2, 3 4] and B = [4 -2, -3 1]. The product AB results in a zero matrix.
Therefore, neither of the statements 1 or 2 is correct. The product of two non-zero matrices can indeed result in an identity matrix or a zero matrix depending on the matrices involved.
1. Product of two non-zero matrices can never be identity matrix:
- This statement is incorrect. The product of two non-zero matrices can result in an identity matrix under certain conditions. For example, if matrix A is invertible and matrix B is its inverse, then the product AB will result in an identity matrix.
2. Product of two non-zero matrices can never be zero matrix:
- This statement is also incorrect. The product of two non-zero matrices can result in a zero matrix. For example, consider two 2x2 matrices A = [1 2, 3 4] and B = [4 -2, -3 1]. The product AB results in a zero matrix.
Therefore, neither of the statements 1 or 2 is correct. The product of two non-zero matrices can indeed result in an identity matrix or a zero matrix depending on the matrices involved.
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Consider the following statements:1. The product of two non-zero matrices can never be identity matrix.2. The product of two non-zero matrices can never be zero matrix.Q. Which of the above statements is/are correct ?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor 2 Correct answer is option 'D'. Can you explain this answer?
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