If A = ((3,1),(7,5)) and A^2 + xI = yA then the values of x and y are ​

Question

If A = \( \begin{pmatrix} 3&1 \\ 7 &5 \end{pmatrix}\) and A² + xI = yA then the values of x and y are

A. X = 6, y = 6 

B. X = 8, y = 8 

C. X = 5, y = 8 

D. X = 6, y = 8

Answer 1

2 + xI = yA

\( \begin{pmatrix} 3&1 \\ 7 &5 \end{pmatrix}\)\( \begin{pmatrix} 3&1 \\ 7 &5 \end{pmatrix}\) + x\( \begin{pmatrix} 1&0 \\ 0 &1 \end{pmatrix}\) = y \( \begin{pmatrix} 3&1 \\ 7 &5 \end{pmatrix}\)

\( \begin{pmatrix} 16&8 \\ 56 &32 \end{pmatrix}\) + x\( \begin{pmatrix} 1&0 \\ 0 &1 \end{pmatrix}\) = y\( \begin{pmatrix} 3&1 \\ 7 &5 \end{pmatrix}\)

8\( \begin{pmatrix} 2&1 \\ 7 &4 \end{pmatrix}\) + x\( \begin{pmatrix} 1&0 \\ 0 &1 \end{pmatrix}\) = y\( \begin{pmatrix} 3&1 \\ 7 &5 \end{pmatrix}\)

Comparing L.H.S and R.H.S 

x = 8 y = 8