Question

Find the value of x ​

Answer 1

If
`A=\left[\begin{array}{cc}a&b\\c&d\end{array}\right]` then
`A^(-1)=\left[\begin{array}{cc}d&-b\\-c&a\end{array}\right]`.

Therefore, if
`A=\left[\begin{array}{cc}x&1\\5&2\end{array}\right]` and
`A^(-1)=\left[\begin{array}{cc}2&-1\\-5&x\end{array}\right]` we can deduce that
`x` can be any number.

Answer 2

Hi,

x=3

Explanation:

`\begin{bmatrix}x & 1 \\5 & 2 \end{bmatrix}*\begin{bmatrix}2 & -1 \\-5 & x \end{bmatrix}=\begin{bmatrix}1 & 0 \\0 & 1 \end{bmatrix}\\\\\\\begin{bmatrix}2x-5 & 0 \\0 & -5+2x \end{bmatrix}=\begin{bmatrix}1 & 0 \\0 & 1 \end{bmatrix}\\\\\\Thus\\2x-5=1\\\\2x=6\\\\\boxed{x=3}\\`