Question:
If for any 2 × 2 square matrix A, we have A ⋅ adj(A) = [8 0; 0 8], then the value of det(A) is:
If for any 2 × 2 square matrix A, we have A ⋅ adj(A) = [8 0; 0 8], then the value of det(A) is:
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Updated On: Apr 23, 2025
- 6
- 5
- 7
- 8
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The Correct Option is D
Solution and Explanation
Step 1: Use the identity
For any square matrix A, the identity is:
A ⋅ adj(A) = det(A) ⋅ I
Step 2: Compare with the given matrix
We are given:
This implies:
det(A) ⋅ I = 8I ⇒ det(A) = 8
Thus, the value of det(A) is 8.
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