Question

If A and B are square matrices of order 3 where $|A|=-2$ and $|B|=1$ then $|\left(A^{-1}\right)adj\left(B^{-1}\right)adj\left(2A^{-1}\right)|$ is equal to

• A. 8
• B. - 8
• C. 1
• D. - 1

Answer 1

The correct option is B - 8

We have $|\left(A^{-1}\right)adj\left(B^{-1}\right)adj\left(2A^{-1}\right)|=\frac{1}{|A|}.\frac{1}{|B{|}^2}.\frac{64}{|A{|}^2}=\frac{64}{-2\times 1\times 4}=-8$
(By using $|A{|}^1=\frac{1}{|A|}$ and $|adjB|=|B{|}^{n-1}$ where n is order of square matrix)