Let $A, B, C, D$ and $E$ be $n \times n$ matrices,each with non-zero determinant. If $ABCDE=I$,then $C^{-1}=$

If $A = \begin{bmatrix} 1 & a \\ 0 & 1 \end{bmatrix}$,then $A^n$ (where $n \in N$) equals

Consider the matrices $A = \begin{bmatrix} 4 & 6 & -1 \\ 3 & 0 & 2 \\ 1 & -2 & 5 \end{bmatrix}$,$B = \begin{bmatrix} 2 & 4 \\ 0 & 1 \\ -1 & 2 \end{bmatrix}$,and $C = \begin{bmatrix} 3 \\ 1 \\ 2 \end{bmatrix}$. Which of the following matrix products are defined?
$(i) (AB)^T C$
$(ii) C^T C (AB)^T$
$(iii) C^T AB$
$(iv) A^T AB B^T C$

If $[m \ n] \begin{bmatrix} m \\ n \end{bmatrix} = [25]$ and $m < n$,then $(m, n) =$

If $A$ and $B$ are square matrices of order $3 \times 3$,$A$ is non-singular,and $AB = O$,then $B$ is a:

If the matrix $\left[\begin{array}{rr}2 & 3 \\ 5 & -1\end{array}\right]=A+B$,where $A$ is symmetric and $B$ is skew-symmetric,then $B$ is equal to