Based on this information answer the questions given below. Two $$n\times n$$ square matrices A and B are said to be similar if there exists a non-singular matrix P such that $$P^{-1}A P=B$$
Let system of linear equations $$\displaystyle a_{1}x+b_{1}y+c_{1}z=d_{1}a_{2}x+b_{2}y+c_{2}z=d_{2}$$ &$$\displaystyle a_{3}x+b_{3}y+c_{3}z=d_{3}$$ can be expressed in the form $$\displaystyle AX=B....(*)$$ where $$\displaystyle A=\begin{pmatrix}a_{1} &b_{1} &c_{1} \\a_{2} &b_{2} &c_{2} \\a_{3} &b_{3} &c_{3} \end{pmatrix}$$ ,$$\displaystyle B=\begin{pmatrix}d_{1}\\d_{2}\\d_{3} \end{pmatrix}$$ $$\displaystyle X= \begin{pmatrix}x\\y\\z\end{pmatrix}$$ The above system of equations (*) is said to be consistent with unique solution if A is non singular & the values of the variables x, y, z can be determined by using the equation $$\displaystyle X= A^{-1} B $$ and if A is singular then system of equations are either consistent with infinitely many solutions or inconsistent with no solution accordingly $$\displaystyle (adj A) (B)= 0 $$ and $$\displaystyle (adj A) (B) \neq 0 $$ where (adj A) is the transpose of cofactor matrix of A Now Assume $$\displaystyle A=\begin{pmatrix} a &1 &0 \\1 &b &d \\1 &b &c\end{pmatrix}$$, $$\displaystyle B= \begin{pmatrix}a &1 &1 \\0 &d &c \\f &g &h \end{pmatrix}$$ $$\displaystyle P=\begin{pmatrix}f\\g\\h\end{pmatrix}$$,$$\displaystyle Q=\begin{pmatrix}a^{2}\\0\\0\end{pmatrix}$$,$$\displaystyle X=\begin{pmatrix}x\\y\\z\end{pmatrix}$$