The number of matrices of order $3 \times 3$,whose entries are either $0$ or $1$ and the sum of all the entries is a prime number,is:

The number of square matrices of order $5$ with entries from the set $\{0, 1\}$,such that the sum of all the elements in each row is $1$ and the sum of all the elements in each column is also $1$,is

$A$ and $B$ are two given matrices such that the order of $A$ is $3 \times 4$. If $A'B$ and $BA'$ are both defined,then:

Let $A$ and $B$ be any two $3 \times 3$ symmetric and skew-symmetric matrices respectively. Then which of the following is $NOT$ true?

$A$ square matrix $[a_{ij}]$ in which $a_{ij} = 0$ for $i \neq j$ and $a_{ij} = k$ (constant) for $i = j$ is called a

If the matrix product $AB = O$,where $O$ is the null matrix,then which of the following is necessarily true?