Question:
Let \( A = \begin{pmatrix} a & 0 \\ c & d \end{pmatrix} \) be a real matrix, where \( ad = 1 \) and \( c \ne 0 \). If \( A^{-1} + (\text{adj} \, A)^{-1} = \begin{pmatrix} \alpha & \beta \\ \gamma & \delta \end{pmatrix} \), then \( (\alpha, \beta, \gamma, \delta) \) is equal to
Let \( A = \begin{pmatrix} a & 0 \\ c & d \end{pmatrix} \) be a real matrix, where \( ad = 1 \) and \( c \ne 0 \). If \( A^{-1} + (\text{adj} \, A)^{-1} = \begin{pmatrix} \alpha & \beta \\ \gamma & \delta \end{pmatrix} \), then \( (\alpha, \beta, \gamma, \delta) \) is equal to
Updated On: Oct 1, 2024
- \( (a + d, 0, 0, a + d) \)
- \( (a + d, 0, c, a + d) \)
- \( (a, 0, 0, d) \)
- \( (a, 0, c, d) \)
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The Correct Option is A
Solution and Explanation
The correct option is (A): \( (a + d, 0, 0, a + d) \)
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