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CBSE Class 12 Math 2011 Solved Paper

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Question : 5 of 29
Marks: +1, -0
Write A−1A^{-1} for A = [2513]\begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix}
Solution:  
A = [2513]\begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix}
A−1A^{-1} = 1∣A∣[3−5−12]\frac{1}{|A|} \begin{bmatrix} 3 & -5 \\ -1 & 2 \end{bmatrix}
= 1[(2×3)−(1×5)]\frac{1}{\left[(2\times 3)-(1\times 5)\right]} [3−5−12]\begin{bmatrix} 3 & -5 \\ -1 & 2 \end{bmatrix}
= 16−5\frac{1}{6-5} [3−5−12]\begin{bmatrix} 3 & -5 \\ -1 & 2 \end{bmatrix}
A−1A^{-1} = [3−5−12]\begin{bmatrix} 3 & -5 \\ -1 & 2 \end{bmatrix}
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