question about 3x3 matrix

[ncc1701d]

Hello
I have this 3 x 3 matrix. I am just learning them and I get confused. Please pardon the verticle line placement. I gets out of wack.

| cos(theta) 0 -sin(theta) |
| 0 1 0 |
| sin(theta) 0 cos(theta) |


and then I have this second matrix below where the sign in "sin(theta)" have switched.
Is the second matrix an "inverse" of the first? or a "transpose" of the first? both or neither?


| cos(theta) 0 sin(theta) |
| 0 1 0 |
| -sin(theta) 0 cos(theta) |



If it was a 2x2 matrix and signs reverse it would be "inverse" but I am uncertain about 3x3 matrix.
thanks.

 

[RisingFury]

In this case, you created a transposed matrix.

The inverse matrix is also not as simple as just switching the sign. Here's a general way of how it's done:

Part 1:
https://www.khanacademy.org/math/al...culating-matrix-of-minors-and-cofactor-matrix

Part 2:
https://www.khanacademy.org/math/al...3-part-2-determinant-and-adjugate-of-a-matrix

 

[ncc1701d]

Great! Thanks. Thats what I needed.

 

[Quick_Nick]

You have a rotation matrix about the Y axis. Rotation matrices happen to be "orthogonal matrices" which means (among other things) that the inverse and transpose are the same.