Let A = [d₁ 0 0; 0 d₂ 0; 0 0 d₃], then A⁻¹ = [d₁⁻¹ 0 0; 0 d₂⁻¹ 0; 0 0 d₃⁻¹] Assertion (A): Let A = [d₁ 0 0; 0 d₂ 0; 0 0 d₃], then A⁻¹ = [d₁⁻¹ 0 0; 0 d₂⁻¹…

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Let A = [d₁ 0 0; 0 d₂ 0; 0 0 d₃], then A⁻¹ = [d₁⁻¹ 0 0; 0 d₂⁻¹ 0; 0 0 d₃⁻¹] Assertion (A): Let 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.

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Answer

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Correct option: (b)

Answer: (b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not correct explanation for Assertion (A).