G Tewani Solutions for Chapter: Matrices, Exercise 1: DPP

If $A\left(\begin{array}{ccc}1& 3& 4\\ 3& -1& 5\\ -2& 4& -3\end{array}\right)=\left(\begin{array}{ccc}3& -1& 5\\ 1& 3& 4\\ 4& -8& 6\end{array}\right)$, then $A=$

Let $A=\left[\begin{array}{ccc}-5& -8& -7\\ 3& 5& 4\\ 2& 3& 3\end{array}\right]$ and $B=\left[\begin{array}{l}x\\ y\\ 1\end{array}\right]$, if $AB=\lambda B \left(\lambda \in R,\lambda \ne 0\right)$ , then the value of $x+y$ can be

$\mathrm{A}=\left[\begin{array}{cc}\mathrm{a}& \mathrm{b}\\ \mathrm{b}& -\mathrm{a}\end{array}\right]$ and $\mathrm{MA}={\mathrm{A}}^{2\mathrm{m}}, \mathrm{m}\in \mathrm{N}$ for some matrix $\mathrm{M}$ then which one of the following is correct?

If $A={\left[a_{ij}\right]}_{m\times n}$, $a_{ij}=\left(i^2+j^2-ij\right)(j-i)$ and $n$ is odd, then which of the following is not the value of $\mathrm{Tr}\left(A\right)$?

$\left|A-B\right|\ne 0, A^4=B^4, C^{3}A=C^{3}B, B^{3}A=A^{3}B,$ then $\left|A^3+B^3+C^3\right|=$

If $AB+BA=0,$ then which of the following is equivalent to $A^3-B^3$.

$A,B,C$ are three matrices of the same order such that any two are symmetric and the $3^{\text{rd}}$ one is skew-symmetric. If $X=ABC+CBA$ and $Y=ABC-CBA,$ then ${\left(XY\right)}^T$ is

If $A$ and $P$ are different matrices of order $n$, satisfying $A^3=P^3$ and $A^{2}P=P^{2}A$ (where $|A-P|\ne 0$) then $\left|A^2+P^2\right|$ is equal to