For Any 2 × 2 Matrix, If a ( a D J a ) = [ 10 0 0 10 ] , Then |A| is Equal to - Mathematics

प्रश्न

For any 2 × 2 matrix, if \[A \left( adj A \right) = \begin{bmatrix}10 & 0 \\ 0 & 10\end{bmatrix}\] , then |A| is equal to ______ .

पर्याय

MCQ

उत्तर

\[A\left( adj A \right) = \begin{bmatrix} 10 & 0\\0 & 10 \end{bmatrix}\]

By definition, we have

\[A\left( adj A \right) = \left| A \right|I = \left( adj A \right)A (\text{ Where I is the identity matrix })\]

\[ \Rightarrow \left| A \right|I = A\left( adj A \right)\]

\[ \Rightarrow \left| A \right|I = 10\begin{bmatrix} 1 & 0\\0 & 1 \end{bmatrix}\]

\[ \Rightarrow \left| A \right| = 10\]

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

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Q 10 Q 9 Q 11

पाठ 7: Adjoint and Inverse of a Matrix - Exercise 7.4 [पृष्ठ ३७]

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आरडी शर्मा Mathematics [English] Class 12

पाठ 7 Adjoint and Inverse of a Matrix
Exercise 7.4 | Q 10 | पृष्ठ ३७

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