If A = \(\left[ \begin{matrix} 3 & 1 \\ 7 & 5 \end{matrix} \right] \) find x, y such that A² +xI = yA Hence find A^-1

If  \(A=\left[ \begin{matrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{matrix} \right] \) Prove that , A =\(\left[ \begin{matrix} { 3 }^{ x-1 } & { 3 }^{ x-1 } & { 3 }^{ x-1 } \\ { 3 }^{ x-1 } & { 3 }^{ x-1 } & { 3 }^{ x-1 } \\ { 3 }^{ x-1 } & { 3 }^{ x-1 } & { 3 }^{ x-1 } \end{matrix} \right] \) for every positive integer n.

The sum of three numbers is -1. If we multiply the second number by 2 , third number by 3 and add them we get 5. If we subtract the third number from the sum of first and second numbers we get -1. Represent it by a system of equations . Find the three numbers using inverse of a matrix