The values of $t$ such that the matrix $\begin{bmatrix} 1 & 3 & 2 \\ 2 & 5 & t \\ 4 & 7 - t & -6 \end{bmatrix}$ has no inverse,are

For two invertible matrices $A$ and $B$ of suitable orders,the value of $(AB)^{-1}$ is

If $A$ is a square matrix of order $3$ such that $\operatorname{det}(A)=3$ and $\operatorname{det}\left(\operatorname{adj}\left(-4 \operatorname{adj}\left(-3 \operatorname{adj}\left(3 \operatorname{adj}\left((2A)^{-1}\right)\right)\right)\right)\right)=2^{m} 3^{n}$,then $m+2n$ is equal to:

If $\begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix} A \begin{bmatrix} -3 & 2 \\ 5 & -3 \end{bmatrix} = I_2$,then $A =$

Matrices $A$ and $B$ will be inverse of each other only if

The inverse of a matrix $A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$ is