Question

If A is a square matrix such that $\left|\begin{array}{ccc}4& 0& 0\\ 0& 4& 0\\ 0& 0& 4\end{array}\right|$=

• A. $4$
• B. $16$
• C. $64$
• D. $256$

Answer 1

The correct option is C $64$

We know that the determinant of a matrix $A=\left[\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right]$ is:

$\left|A\right|=a(ei-fh)-b(di-fg)+c(dh-eg)$

Here, the given matrix is $A=\left[\begin{array}{ccc}4& 0& 0\\ 0& 4& 0\\ 0& 0& 4\end{array}\right]$, so, let us find the determinant of matrix $A$ as shown below:

$\left|A\right|=4\left[\right(4\times 4)-(0\times 0\left)\right]-0\left[\right(0\times 4)-(0\times 0\left)\right]+0\left[\right(0\times 0)-(0\times 4\left)\right]=4(16-0)-0(0-0)+0(0-0)$

$=4\times 16=64$

Hence, the determinant of the matrix $\left[\begin{array}{ccc}4& 0& 0\\ 0& 4& 0\\ 0& 0& 4\end{array}\right]$ is $64$.