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Let the matrices and be such that .

Assertion: Let the matrices $A = \begin{bmatrix} -3 & 2 \\ -5 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} 4 & -2 \\ 5 & -3 \end{bmatrix}$ be such that $A^{100}B = BA^{100}$.

Reason: $AB = BA$ implies $A^n B = BA^n$ for all positive integers $n$.

• (a)Both Assertion and Reason are true and Reason is the correct explanation for Assertion.
• (b)Both Assertion and Reason are true but Reason is not the correct explanation for Assertion.
• (c)Assertion is true and Reason is false.
• (d)Assertion is false and Reason is true.

Answer

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From ISC 2024 Mathematics Paper 1, question 1(vii).