Question

If A is a square matrix of order 3 and $\left| A \right| = 4$. Find the value of $\left| {2A} \right|$.

Answer 1

Hint: To solve this we should have knowledge of properties of determinant and matrices like if A is $n \times n$ matrix then $\left| {KA} \right| = {k^n}\left| A \right|$. If we use this property, the question becomes too easy.

Complete step-by-step answer:

We have a square matrix A of order 3.
From given:
$\left| A \right| = 4$ and we have to find $\left| {2A} \right|$
To solve this question we will use the property that if A is a square matrix of order $n \times n$ then $\left| {KA} \right| = {k^n}A$ .
Here in this question k is 2 , so here $\left| {2A} \right| = {2^n}\left| A \right| = {2^3}\left| A \right|$ ( because here n is 3)
So we have $\left| {2A} \right| = {2^3}\left| A \right| = 8 \times 4 = 32{\text{ }}\left( {\because \left| A \right| = 4} \right)$
So 32 is the final answer we get.

Note: Whenever we get this type of question the key concept of solving is we have to ensure that by using which property of matrices and determinant we can solve this question if we are able to identify that this is the perfect property applicable on this question then there is nothing left in the question that becomes question becomes easy.