Choose the correct answer. Let A be a square matrix of order 3×3,then IkAI is equal to
\(K \mid A \mid\)
\(K^2\mid A\mid\)
\(K^3\mid A\mid\)
\(3K \mid A\mid\)
A is a square matrix of order 3 × 3.
Let A=\(\begin{bmatrix}a_1&b_1&c_1\\a_2&b_2&c_2\\a_3&b_3&c_3\end{bmatrix}\)
Then kA=\(\begin{bmatrix}ka_1&kb_1&kc_1\\ka_2&kb_2&kc_2\\ka_3&kb_3&kc_3\end{bmatrix}\)
so IkAI=\(\begin{vmatrix}ka_1&kb_1&kc_1\\ka_2&kb_2&kc_2\\ka_3&kb_3&kc_3\end{vmatrix}\)
=k3 \(\begin{vmatrix}a_1&b_1&c_1\\a_2&b_2&c_2\\a_3&b_3&c_3\end{vmatrix}\)
=k3IAI
so IkAI=k3IAI
Hence, the correct answer is C.
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