Question

let A=(3 x)
(-2 -3)
if A=A^-1, what is x?


please show work so i can understand

Answer 1

Is (3 x) a 2 x 1 matrix?
What is the meaning of the second line, (-2 -3)? It just sits there.

Is the A matrix in the first line supposed to operate on (3 x) ?

(3 x) and (-2 -3) cannot be multiplied.
One has ti be a column vector.

Answer 2

The second line is probably meant to be the second row of the 2x2 matrix.

I.e. A=
(3 x}
(-2 -3)

If A=A^-1, then
A^-1A = I

(3 x} (3 x}
(-2 -3)(-2 -3) = I

Performing the matrix multiplication:
(9-2x 0)
(0 -2x+9) = I

so
9-2x=1
or x=4

Substitute x=4 and redo the matrix multiplication to make sure that the result is a 2x2 identity matrix.