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Can you explain the answer of this question below:
If A and B are invertible matrices of order 3 , then det (adj A) =
- A:(detA)2
- B:1
- C:A−1
- D:none of these
The answer is d.
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Can you explain the answer of this question below:If A and B are inver...
Let A be a non singular square matrix of order n . then , |adj.A| = A−1
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Can you explain the answer of this question below:If A and B are inver...
The correct answer is a) (det A)^2.
To prove this, let's start by recalling the properties of the adjugate matrix. The adjugate matrix of A, denoted as adj A, is defined as the transpose of the cofactor matrix of A.
The cofactor matrix of A, denoted as cof A, is obtained by taking the determinant of each 2x2 submatrix of A, multiplying it by (-1) raised to the power of the sum of its row and column indices, and then transposing the resulting matrix.
Now, we know that A is an invertible matrix of order 3. This means that det A is not equal to 0.
Since A is invertible, each element of the cofactor matrix, cof A, is nonzero. Therefore, each element of the adjugate matrix, adj A, is also nonzero.
Now, let's consider the determinant of adj A. By definition, the determinant of adj A is the product of the diagonal elements of adj A. Since each element of adj A is nonzero, the determinant of adj A is also nonzero.
Now, let's consider the determinant of det A. Since A is invertible, det A is not equal to 0. Therefore, (det A)^2 is also nonzero.
Since both (det A)^2 and det adj A are nonzero, they must be equal. Therefore, the correct answer is a) (det A)^2.
To prove this, let's start by recalling the properties of the adjugate matrix. The adjugate matrix of A, denoted as adj A, is defined as the transpose of the cofactor matrix of A.
The cofactor matrix of A, denoted as cof A, is obtained by taking the determinant of each 2x2 submatrix of A, multiplying it by (-1) raised to the power of the sum of its row and column indices, and then transposing the resulting matrix.
Now, we know that A is an invertible matrix of order 3. This means that det A is not equal to 0.
Since A is invertible, each element of the cofactor matrix, cof A, is nonzero. Therefore, each element of the adjugate matrix, adj A, is also nonzero.
Now, let's consider the determinant of adj A. By definition, the determinant of adj A is the product of the diagonal elements of adj A. Since each element of adj A is nonzero, the determinant of adj A is also nonzero.
Now, let's consider the determinant of det A. Since A is invertible, det A is not equal to 0. Therefore, (det A)^2 is also nonzero.
Since both (det A)^2 and det adj A are nonzero, they must be equal. Therefore, the correct answer is a) (det A)^2.
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Can you explain the answer of this question below:If A and B are invertible matrices of order 3 , then det (adj A) =A:(detA)2B:1C:A−1D:none of theseThe answer is d.
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Can you explain the answer of this question below:If A and B are invertible matrices of order 3 , then det (adj A) =A:(detA)2B:1C:A−1D:none of theseThe answer is d. for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Can you explain the answer of this question below:If A and B are invertible matrices of order 3 , then det (adj A) =A:(detA)2B:1C:A−1D:none of theseThe answer is d. covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Can you explain the answer of this question below:If A and B are invertible matrices of order 3 , then det (adj A) =A:(detA)2B:1C:A−1D:none of theseThe answer is d..
Can you explain the answer of this question below:If A and B are invertible matrices of order 3 , then det (adj A) =A:(detA)2B:1C:A−1D:none of theseThe answer is d. for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Can you explain the answer of this question below:If A and B are invertible matrices of order 3 , then det (adj A) =A:(detA)2B:1C:A−1D:none of theseThe answer is d. covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Can you explain the answer of this question below:If A and B are invertible matrices of order 3 , then det (adj A) =A:(detA)2B:1C:A−1D:none of theseThe answer is d..
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