Question:
If B is the inverse of a third order matrix A and det B = k, then $(\text{adj}(\text{adj} A))^{-1}=$
If B is the inverse of a third order matrix A and det B = k, then $(\text{adj}(\text{adj} A))^{-1}=$
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Remember that the adjoint matrix and inverse are closely related through the determinant, and properties of determinants help simplify expressions involving adjoints.
Updated On: Jun 6, 2025
- $kB$
- $\frac{1}{k}B$
- $kB^{-1}$
- $B + kI$
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The Correct Option is A
Solution and Explanation
Given $B = A^{-1}$, and $\det B = k$. Recall that $\text{adj}(A) = \det(A) A^{-1}$. Applying this repeatedly and properties of determinants, we find that $(\text{adj}(\text{adj} A))^{-1} = kB$.
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