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

The Correct Option is C

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.