If A is a square matrix such that A (adj A) = 10I, then $|A|$ = ____________________.

Open in App

Solution

Given:
A is a square matrix
A(adj A) = 10I

As we know,
$A (adj A) = |A| I \Rightarrow 10 I = |A| I \Rightarrow |A| = 10$

Hence, $|A| = 10$ .

Suggest Corrections

Similar questions

A

3

A (a d j A) = 10 I

[\begin{matrix} 10 & 0 \\ 0 & 10 \end{matrix}], then |A|

A (A d j A) = ⎡ ⎢ ⎣ \begin{matrix} 4 & 0 & 0 0 & 4 & 0 0 & 0 & 4 \end{matrix} ⎤ ⎥ ⎦

\frac{| A d j (A d j A)}{| A d j A |}

A

A (A d j A) = ⎛ ⎜ ⎝ \begin{matrix} 4 & 0 & 0 0 & 4 & 0 0 & 0 & 4 \end{matrix} ⎞ ⎟ ⎠

(A d j A) =

A a d j A = d i a g (k, k, k)

| a d j A | =

Join BYJU'S Learning Program