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Let , then Assertion (A): Let , then Reason (R): If is a diagonal matrix, then exists, it is also a…
Assertion: Let $A = \begin{bmatrix} d_1 & 0 & 0 \\ 0 & d_2 & 0 \\ 0 & 0 & d_3 \end{bmatrix}$, then $A^{-1} = \begin{bmatrix} d_1^{-1} & 0 & 0 \\ 0 & d_2^{-1} & 0 \\ 0 & 0 & d_3^{-1} \end{bmatrix}$
Reason: If $A$ is a diagonal matrix, then $A^{-1}$ exists, it is also a diagonal matrix.
Assertion (A): Let $A = \begin{bmatrix} d_1 & 0 & 0 \\ 0 & d_2 & 0 \\ 0 & 0 & d_3 \end{bmatrix}$, then $A^{-1} = \begin{bmatrix} d_1^{-1} & 0 & 0 \\ 0 & d_2^{-1} & 0 \\ 0 & 0 & d_3^{-1} \end{bmatrix}$
Reason (R): If $A$ is a diagonal matrix, then $A^{-1}$ exists, it is also a diagonal matrix.
- (a)Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation for Assertion (A).
- (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation for Assertion (A).
- (c)Assertion (A) is true, and Reason (R) is false.
- (d)Assertion (A) is false, and Reason (R) is true.
Answer
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From ISC 2025 Practice Mathematics, question 37.