Find x such that the matrix is equal to its own inverse. A = left[3 x , -2 -3right]

Question
Matrices
asked 2021-02-25
Find x such that the matrix is equal to its own inverse.
\(A = \left[3 x , -2 -3\right]\)

Answers (1)

2021-02-26
When you multiply this matrix by itself, the first element is 9-2x that has to be equal to 1.
\(9-2x=1\)
\(-2x=-8\)
\(x=4\)
So the answer \(x = 4\) then the matrix is its own inverse!
\(\left[\left[3,x\right],\left[-2,-3\right]^2=\left[\left[9-2x,3x-3x\right],\left[-6+6\right],\left[-2x+9\right]\right]\right]\)
when \(x = 4\) then
\(\begin{bmatrix}1 & 0 \\0 & 1 \end{bmatrix}\)
Result: \(x = 4\)
0

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