If a = ⎡ ⎢ ⎣ a 0 0 0 a 0 0 0 a ⎤ ⎥ ⎦ , Then the Value of |Adj A| is - Mathematics

Question

If \[A = \begin{bmatrix}a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a\end{bmatrix}\] , then the value of |adj A| is _____________ .

Options

a²⁷
a⁹
a⁶
a²

MCQ

Solution

a⁶

\[A = \begin{bmatrix} a & 0 & 0\\0 & a & 0\\0 & 0 & a \end{bmatrix}\]

\[ \therefore \left| A \right| = \begin{bmatrix} a & 0 & 0\\0 & a & 0\\0 & 0 & a \end{bmatrix} = a^3 \neq 0\]

and

\[n = 3\]

Thus, we have

\[\left| adj A \right| = \left| A \right|^{n - 1} = \left( a^3 \right)^2 = a^6 \]

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Properties of Matrix Multiplication - Inverse of a Square Matrix by the Adjoint Method

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Q 7 Q 6 Q 8

Chapter 7: Adjoint and Inverse of a Matrix - Exercise 7.4 [Page 37]

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RD Sharma Mathematics [English] Class 12

Chapter 7 Adjoint and Inverse of a Matrix
Exercise 7.4 | Q 7 | Page 37

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