Let \(\mathbf{A}, \mathbf{B}, \mathbf{C}\) and \(\mathbf{D}\) be the following matrices: \(\begin{align*} &\mathbf{A} \text{ sends every vector to the zero vector}, \\ &\mathbf{B} \text{ reflects vectors across the $xz$-plane}, \\ &\mathbf{C} \text{ projects vectors onto the vector $\mathbf{i}+ 3 \mathbf{k}$}, \\ &\mathbf{D} \text{ sends every vector to twice itself}. \end{align*}\)

For each matrix above, figure out whether it's invertible, and answer "yes" or "no" in the order above. (Answer with "yes" if it is invertible.)

Could someone help? I'm not sure how to figure out whether it's invertible or not!

rubikx2910 Mar 2, 2020