Question

For a invertible matrix A if A(adjA) = ${\displaystyle \left[\begin{array}{cc}10& 0\\ 0& 10\end{array}\right]}$, then |A| = ______.

विकल्प

• 100

• –100

• 10

• –10

Answer 1

For a invertible matrix A if A(adjA) = ${\displaystyle \left[\begin{array}{cc}10& 0\\ 0& 10\end{array}\right]}$, then |A| = 10.

Explanation:

We have,

A(adjA) = ${\displaystyle \left[\begin{array}{cc}10& 0\\ 0& 10\end{array}\right]=10\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]}$ = 10I

As, A(adjA) = |A| I

After comparing on both sides, we get

|A| = 10