The number of all possible matrices of order $3 \times 3$ with each entry $0$ or $1$ is:

For two $3 \times 3$ matrices $A$ and $B$,let $A + B = 2B^T$ and $3A + 2B = I_3$,where $B^T$ is the transpose of $B$ and $I_3$ is the $3 \times 3$ identity matrix. Then:

Express the following matrix as the sum of a symmetric and a skew-symmetric matrix: $\left[\begin{array}{cc}3 & 5 \\ 1 & -1\end{array}\right]$

If a matrix has $8$ elements,what are the possible orders it can have?

Let $A = \begin{bmatrix} 0 & 1 \\ 1 & k \end{bmatrix}$, $k \in R$ and $A^3 = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$. If $d = 228$, then $b + c =$

If $A = \begin{bmatrix} 0 & 2 \\ 3 & -4 \end{bmatrix}$ and $kA = \begin{bmatrix} 0 & 3a \\ 2b & 24 \end{bmatrix}$,then the values of $k, a, b$ are respectively