Questions: A=[9 2 6; -4 -5 -6] (A^T)^T=

A=[9 2 6; -4 -5 -6] (A^T)^T=
Transcript text: A=\left[\begin{array}{ccc}9 & 2 & 6 \\ -4 & -5 & -6\end{array}\right] \\ \left(A^{T}\right)^{T}=
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Solution

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Solution Steps

To solve this problem, we need to understand the properties of matrix transposition. The transpose of a transpose of a matrix returns the original matrix. Therefore, \((A^T)^T = A\).

Step 1: Understanding Matrix Transposition

The problem involves the matrix \( A \) given by: \[ A = \begin{bmatrix} 9 & 2 & 6 \\ -4 & -5 & -6 \end{bmatrix} \]

Step 2: Applying Transposition Properties

The property of matrix transposition states that the transpose of the transpose of a matrix returns the original matrix: \[ (A^T)^T = A \]

Step 3: Result Verification

Given the property, we verify that: \[ (A^T)^T = \begin{bmatrix} 9 & 2 & 6 \\ -4 & -5 & -6 \end{bmatrix} \]

Final Answer

\[ \boxed{\begin{bmatrix} 9 & 2 & 6 \\ -4 & -5 & -6 \end{bmatrix}} \]

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