Which statement correctly describes the condition for two square matrices, $A$ and $B$, to be multiplicative inverses of each other?

Their product $A \cdot B$ is the identity matrix $I$.

Their sum $A + B$ is the identity matrix $I$.

Their product $A \cdot B$ is a matrix of all zeros.

Each element in $B$ is the reciprocal of the corresponding element in $A$.

Are the matrices $C = \begin{bmatrix} 4 & 9 \\ 1 & 2 \end{bmatrix}$ and $D = \begin{bmatrix} -2 & 9 \\ 1 & -4 \end{bmatrix}$ inverses of each other?

Yes, because their product is the identity matrix.

No, because their product is $\begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$.

No, because their product is a zero matrix.

Yes, because their determinants are both 1.

No, their product is not the identity matrix.

Yes, their product is the identity matrix.

No, because you cannot multiply these matrices.

Yes, because their determinants are opposites.