Question

Choose the correct answer. Let A be a square matrix of order 3×3,then IkAI is equal to

• A. $K \mid A \mid$
• B. $K^2\mid A\mid$
• C. $K^3\mid A\mid$
• D. $3K \mid A\mid$

Answer 1

Answer: (C)

$K^3\mid A\mid$

Answer 2

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.