Answer:
Option B
Step-by-step explanation:
Property of the multiplicative inverse,
A × A⁻¹ = I
Here A⁻¹ is the inverse of matrix A and I = Identity matrix.
Option A
[tex]\begin{bmatrix}1 & -3\\ 1 & -4\end{bmatrix}\times \begin{bmatrix}4 & -3\\ 1 & 1\end{bmatrix}=\begin{bmatrix}1 & -6\\ 0 & -7\end{bmatrix}[/tex]
False
Option B
[tex]\begin{bmatrix}1 & 3\\ 1 & 4\end{bmatrix}\times \begin{bmatrix}4 & -3\\ -1 & 1\end{bmatrix}=\begin{bmatrix}1 & 0\\ 0 & 1\end{bmatrix}[/tex]
True
Option C
[tex]\begin{bmatrix}-1 & 3\\ -1 & 4\end{bmatrix}\times \begin{bmatrix}4 & -3\\ 1 & 1\end{bmatrix}=\begin{bmatrix}-1 & 6\\ 0 & 7\end{bmatrix}[/tex]
False
Option D
[tex]\begin{bmatrix}1 & -3\\ -1 & 4\end{bmatrix}\times \begin{bmatrix}4 & -3\\ 1 & 1\end{bmatrix}=\begin{bmatrix}1 & -6\\ 0 & 7\end{bmatrix}[/tex]
False
Option B is the correct option.
