Question

Let \( A=\left[\begin{array}{cc}1 & -1 \\ 4 & 2\end{array}\right] \), if \( A^{-1}=\alpha A+\beta I \), I is \( 2 \times 2 \) identify matrix, then \( \frac{\alpha}{\beta} \) is: (A) \( -\frac{1}{3} \) (B) 2 (C) 3 (D) 6

Answer 1

This is a very nice little problem involving matrices.  Solving we get:

 a = -1/6  and b = 1/2   which leads to  a/b = -1/3

So the correct answer is: (A) -1/3

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