Question

Which matrices are multiplicative inverses?

Answer 1

Option B

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

`\begin{bmatrix}1 & -3\\ 1 & -4\end{bmatrix}* \begin{bmatrix}4 & -3\\ 1 & 1\end{bmatrix}=\begin{bmatrix}1 & -6\\ 0 & -7\end{bmatrix}`

False

Option B

`\begin{bmatrix}1 & 3\\ 1 & 4\end{bmatrix}* \begin{bmatrix}4 & -3\\ -1 & 1\end{bmatrix}=\begin{bmatrix}1 & 0\\ 0 & 1\end{bmatrix}`

True

Option C

`\begin{bmatrix}-1 & 3\\ -1 & 4\end{bmatrix}* \begin{bmatrix}4 & -3\\ 1 & 1\end{bmatrix}=\begin{bmatrix}-1 & 6\\ 0 & 7\end{bmatrix}`

False

Option D

`\begin{bmatrix}1 & -3\\ -1 & 4\end{bmatrix}* \begin{bmatrix}4 & -3\\ 1 & 1\end{bmatrix}=\begin{bmatrix}1 & -6\\ 0 & 7\end{bmatrix}`

False

Option B is the correct option.