Properties of Inverse of a Matrix

If $A$ and $B$ are square matrices of order $3$ then

If $A$ and $B$ are matrices and $B=AB{A}^{-1}$, then the value of $\left(A+B\right)\left(A-B\right)$ is

If $A=\left[\begin{array}{cc} 2& 2\\ -3& 2\end{array}\right]$ and $B=\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right],$ then ${\left(B^{-1}{A}^{-1}\right)}^{-1}=$

If $A$ and $B$ are square matrices of the same order and $A$ is non-singular, then for a positive integer $n,{\left(A^{-1}BA\right)}^n$ is equal to 

If a matrix $A$ is such that $4A^3+2A^2+7A+I=0$, then $A^{-1}$ equals

If $P=\left[\begin{array}{lll}1& 2& 3\\ 3& 1& 0\\ 0& 0& 1\end{array}\right], Q=\left[\begin{array}{ccc}1& -2& -3\\ -3& 1& 9\\ 0& 0& -5\end{array}\right]$, then $(PQ{)}^{-1}$ equals to

If product of matrix $A$ with $\left[\begin{array}{cc}0& 1\\ 2& -4\end{array}\right]$ is $\left[\begin{array}{ll}3& 2\\ 1& 1\end{array}\right]$, then $A^{-1}$ is given by

If $D=diag\left[2, 3, 4\right]$, then $D^{-1}=$

If $A=\left[\begin{array}{lll}1& 2& 2\\ 2& 1& 2\\ 2& 2& 1\end{array}\right]$ and $A^{-1}$ exists and not equal to zero, then $\left(A^2-4A\right)A^{-1}$ is

Let $A$ be an invertible matrix. Which of the following is not true?

From the matrix equation $AB=AC$ we can conclude that $B=C$, provided
 

Let $A, B$ and $C$ are $n\times n$ matrices such that $\left|A\right|=2, \left|B\right|=3$ and $\left|C\right|=5.$ If $\left|{\left(2A\right)}^2\left(3B\right){\left(5C\right)}^{-1}\right|=\frac{1728}{125}$, then the value of $n$ is equal to