Let $$A = \left[ {\matrix{ 1 & 2 \cr { - 1} & 4 \cr } } \right]$. If A$-$1 = $\alpha$I + $\beta$A, $\alpha$, $\beta$ $\in$ R, I is a 2 $\times$ 2 identity matrix then 4($\alpha$ $-$ $\beta$$) is equal to :

Question

Let $$A = \left[ {\matrix{ 1 & 2 \cr { - 1} & 4 \cr } } \right]$. If A^$-$1 = $\alpha$I + $\beta$A, $\alpha$, $\beta$ $\in$ R, I is a 2 $\times$ 2 identity matrix then 4($\alpha$ $-$ $\beta$$) is equal to :

${8 \over 3}$

Solution

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