Find the matrix X satisfying the equation:[(2 ,1), (5, 3)]X[(5, 3), (3, 2)] = [(1, 0), (0, 1)]

Question

Find the matrix X satisfying the equation:

\(\begin{bmatrix}2&1\\5&3\end{bmatrix}X\begin{bmatrix}5&3\\3&2\end{bmatrix}\)\(=\begin{bmatrix}1&0\\0&1\end{bmatrix}.\)

Answer 1

 \(A=\begin{bmatrix}2&1\\5&3\end{bmatrix}\)\(B=\begin{bmatrix}5&3\\3&2\end{bmatrix}\)\(C=\begin{bmatrix}1&0\\0&1\end{bmatrix}\)

Then The given equations becomes as

AXB = I

= X = A^-1 B^–1

|A| = 6 – 5 = 1

|B| = 10 – 9 = 1