Question

Given matrices G and H below, which statement is true?

Answer 1

Answer:

Option B.

Step-by-step explanation:

The given matrices are

$G=\begin{bmatrix}7&5\\ \:4&3\end{bmatrix}$

$H=\begin{bmatrix}-6&-5\\ \:-4&-2\end{bmatrix}$

Two matrices are inverse of each other if product of both matrices is identity matrix, i.e., $I=\begin{bmatrix}1&0\\ \:0&1\end{bmatrix}$.

$\begin{bmatrix}7&5\\ \:4&3\end{bmatrix}\begin{bmatrix}-6&-5\\ \:-4&-2\end{bmatrix}$

$\begin{bmatrix}7\left(-6\right)+5\left(-4\right)&7\left(-5\right)+5\left(-2\right)\\ 4\left(-6\right)+3\left(-4\right)&4\left(-5\right)+3\left(-2\right)\end{bmatrix}$

$\begin{bmatrix}-62&-45\\ -36&-26\end{bmatrix}\neq I$

Matrices G and H are not inverses of each other because GH does not equal I.

Therefore, the correct option is B.

Answer 2

E I just took the test