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# Solution for If a is a Square Matrix Such that a ( a D J a ) = ⎡ ⎢ ⎣ 5 0 0 0 5 0 0 0 5 ⎤ ⎥ ⎦ , Then Write the Value of |Adj A|. - CBSE (Commerce) Class 12 - Mathematics

#### Question

If A is a square matrix such that $A \left( adj A \right) = \begin{bmatrix}5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5\end{bmatrix}$ , then write the value of |adj A|.

#### Solution

$\text{ Given: }\hspace{0.167em} A\left( adj A \right) = \begin{bmatrix} 5 & 0 & 0\\0 & 5 & 0\\0 & 0 & 5 \end{bmatrix}$
$\Rightarrow \hspace{0.167em} \left| A \right| I_n = 5\begin{bmatrix} 1 & 0 & 0\\0 & 1 & 0\\0 & 0 & 1 \end{bmatrix}$
$\Rightarrow \hspace{0.167em} \left| A \right| = 5$
$\text{Now,}\left| adj A \right| = \hspace{0.167em} \left| A \right|^{n - 1} = 5^{3 - 1} = 25$

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#### APPEARS IN

R.D. Sharma Mathematics for Class 12 by R D Sharma (Set of 2 Volume) (2018-19 Session) (with solutions)
Chapter 8: Solution of Simultaneous Linear Equations
Q: 18 | Page no. 35

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Solution for question: If a is a Square Matrix Such that a ( a D J a ) = ⎡ ⎢ ⎣ 5 0 0 0 5 0 0 0 5 ⎤ ⎥ ⎦ , Then Write the Value of |Adj A|. concept: Determinant of a Square Matrix. For the courses CBSE (Commerce), CBSE (Arts), PUC Karnataka Science, CBSE (Science)
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