G Tewani Solutions for Chapter: Matrices, Exercise 2: DPP

Let $A$ be a $2\times 3$ matrix, while $B$ be a $3\times 2$ matrix. If $\left|AB\right|=4$, then the value of $\left|BA\right|$ is

Let $A$ be a square matrix of order $3$, so that sum of elements of each row is $1$. Then, the sum of elements of matrix $A^2$ is

Let $A$ and $B$ be $3\times 3$ matrices such that $AB+A+B=0$, then

If $(A+B{)}^2=A^2+B^2$ and $\lfloor A|\ne 0$ (where $A$ and $B$ are matrices of odd order), then $\left|B\right|=$?

If $A=\left[\begin{array}{lll}1& 0& 0\\ 1& 0& 1\\ 0& 1& 0\end{array}\right]$, then

If the elements of a $2\times 2$ matrix $A$ are real, positive, and distinct such that $det{\left(A+A^{\mathit{T}}\right)}^T=0$, then

If $A=\left[\begin{array}{ccc}8& -6& 2\\ -6& 7& -4\\ 2& -4& 3\end{array}\right]$ and $X$ is a non zero column matrix, such that $AX=\lambda X$, where $\lambda$ is a scalar, then the values of $\lambda$ can be

If $A$ and $B$ are two square matrices of the same order, such that $A+B=AB$ and $I$ is the identity matrix of the order same as that of $A$ and $B$, then