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The matrix is $\begin{bmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ -1 & 0 & 0 \end{bmatrix}$. This is derived by tracking the standard basis vectors: $\hat{i}$ moves to $(0, 0, -1)$, $\hat{j}$ remains stationary at $(0, 1, 0)$, and $\hat{k}$ swings to $(1, 0, 0)$.

Conditions: Rotation is 90 degrees around the y-axis.; Working in a right-handed 3D coordinate system.

The matrix is $\begin{bmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ -1 & 0 & 0 \end{bmatrix}$. This is derived by tracking the standard basis vectors: $\hat{i}$ moves to $(0, 0, -1)$, $\hat{j}$ remains stationary at $(0, 1, 0)$, and $\hat{k}$ swings to $(1, 0, 0)$.

Conditions: Rotation is 90 degrees around the y-axis.; Working in a right-handed 3D coordinate system.

To construct the 3x3 matrix, observe where the three standard basis vectors ($\hat{i}$, $\hat{j}$, and $\hat{k}$) land after the transformation. Record the final coordinates of these transformed vectors as column vectors.

Conditions: Working in three-dimensional Cartesian space.; The transformation is linear.

To construct the 3x3 matrix, observe where the three standard basis vectors ($\hat{i}$, $\hat{j}$, and $\hat{k}$) land after the transformation. Record the final coordinates of these transformed vectors as column vectors.

Conditions: Working in three-dimensional Cartesian space.; The transformation is linear.