Question

Let $A$ is a square matrix of order $n$ and $a$ being a scalar then $|aA|=$

• A. $a|A|$
• B. $|a||A|$
• C. $a^n|A|$
• D. none of these

Answer 1

The correct option is C $a^n|A|$

Given, $A$ is a square matrix of order $n$ and $a$ being a scalar.

Now $aA$ is the matrix in which each elements of $A$ is multiplied by $a$.

So when we take determinant of $aA$ then form each row or column $a$ will be common.

Then $|aA|=a^n|A|$.