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  4. If A = [a&0&0 0&a&0 0&0&a], then det(adj A) is

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Q. If $A = \begin{bmatrix}a&0&0\\ 0&a&0\\ 0&0&a\end{bmatrix}$, then det(adj A) is

COMEDKCOMEDK 2015Matrices

Solution:

Since $A = \begin{bmatrix}a&0&0\\ 0&a&0\\ 0&0&a\end{bmatrix}$
$ \Rightarrow \:\:\:\: |A| = a.a.a =a^3$
Using formula $[adj \, Al = |A|^{n-1}$, we get det $(adj \, A)= (a^3)^{3-1} = (a^3)^2 = a^6$