A = \(\begin{bmatrix}-1&1&1\\1&-1&1\\1&1&-1\end{bmatrix}\)

|A| = -1 + 1 + 1 + 1 + 1 + 1 = 4

Now,

|2 adj (3adj(4A^{-1}))| = 2^{3}|adj(3adj (4A^{-1}))|

(\(\because\) |KA| = K^{n}|A|)

= 2^{3}|3adj(4A^{-1})|^{2} (\(\because\) |adj A| = |A|^{n-1})

= 2^{3}(3^{3}|adj (4A^{-1})|)^{2}** (\(\because\) |KA| = K**^{n}|A|)

= 2^{3}.3^{6} |adj(4A^{-1})|^{4}

= 2^{3}.3^{6}(4^{3}. (A^{-1}))^{4} **(\(\because\) |KA| = K**^{n}|A|)

= ** **2^{3}.3^{6}(4^{3}. \(\frac14\)) (**\(\because\)** |A^{-1}| = \(\frac1{|A|}=\frac14\))

= 2^{3}.3^{6}(4^{2})^{4}

= 2^{3}.3^{6}.4^{8}

= 2^{3}.3^{6}.2^{16}

= 2^{19}.3^{6}

\(\therefore\) a = 19, b = 6

\(\therefore\) a - 2b = 19 - 12 = 7