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Let A be a square matrix of order 3xx3, ...

Let A be a square matrix of order `3xx3`, then `|k A|`is equal to
(A) `k|A|` (B) `k^2|A|` (C) `K^3|A|` (D) `3k |A|`

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AI Generated Solution

To solve the problem, we need to find the determinant of the matrix \( kA \), where \( A \) is a square matrix of order \( 3 \times 3 \) and \( k \) is a scalar. ### Step-by-step Solution: 1. **Understanding the Matrix \( kA \)**: - If \( A \) is a \( 3 \times 3 \) matrix, then multiplying \( A \) by a scalar \( k \) means that every element of the matrix \( A \) is multiplied by \( k \). - Thus, if \( A = \begin{pmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{pmatrix} \), then \( kA = \begin{pmatrix} k a_{11} & k a_{12} & k a_{13} \\ k a_{21} & k a_{22} & k a_{23} \\ k a_{31} & k a_{32} & k a_{33} \end{pmatrix} \). ...
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