Question

Please help! Correct answer only, please! Given matrix A and B both have dimensions 2 x 2 and are the inverse of one another what should be the following product? A · B A. B. C. D.

Answer 1

Answer:

Option B.

Step-by-step explanation:

Let the two matrix A and $A^{-1}$ are,

A = $\begin{bmatrix}4 & 3\\ 3 & 2\end{bmatrix}$ and $A^{-1}$ = $\frac{1}{(-1)}$$\begin{bmatrix}2 &-3\\-3 & 4\end{bmatrix}$

Therefore, $A^{-1}$ = $\begin{bmatrix}-2 & 3\\3 & -4\end{bmatrix}$

Now $A.A^{-1}$ = $\begin{bmatrix}4 & 3\\ 3 & 2\end{bmatrix}.\begin{bmatrix}-2 & 3\\3 & -4\end{bmatrix}$

                   = $\begin{bmatrix}(-8+9) & (12-12)\\(-6+6) & (9-8)\end{bmatrix}$

                  = $\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}$

Therefore, Option (B) will be the answer.