Question

The matrix $P=\left[\begin{array}{ccc}0& 0& 4\\ 0& 4& 0\\ 4& 0& 0\end{array}\right]$ is a

• A. Diagonal Matrix
• B. Square Matrix
• C. Unit Matrix
• D. Zero

Answer 1

The correct option is B Square Matrix

$\text{Given}P=\left[\begin{array}{ccc}0& 0& 4\\ 0& 4& 0\\ 4& 0& 0\end{array}\right]$

Checking for square matrix.
$\text{Number of Rows in}P=3$
$\text{Number of Columns in}P=3$
$\Rightarrow \text{No. of rows}=\text{No. of columns}$
So, $P$ is a square matrix.

Checking for diagonal matrix.
A diagonal matrix is a square matrix, where all of its non-diagonal elements are zero. Since $P$ is a square matrix but its all non-diagonal elements are not zero, hence matrix $P$ is not a diagonal matrix.

Checking for unit matrix.
A unit matrix is a square matrix in which elements in the diagonal are all 1 and rest are all zeroes. Since 𝑃 is a square matrix but it has neither all diagonal elements as 1 nor all other elements as zeroes, hence $P$ is not a unit matrix.

Checking for zero matrix.
A unit matrix is a square matrix in which all the elements are zeroes. The matrix $P$ is having the non-zero entry $4$. Hence $P$ is not a zero matrix.

Hence Option (A) is correct.