216k views
4 votes
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.

Please help! Correct answer only, please! Given matrix A and B both have dimensions-example-1

1 Answer

2 votes

Answer:

Option B.

Explanation:

Let the two matrix A and
A^(-1) are,

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

User Jstruzik
by
8.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories