MATH SOLVE

3 months ago

Q:
# Given matrices G and H below, which statement is true?G= 7 5 4 3 H= -6 -5 -4 -2A.) Matrices G and H are not inverses of each other because G + H does not equal I.B.) Matrices G and H are not inverses of each other because GH does not equal I.C.) Matrices G and H are inverses of each other because GH = I.E.) Matrices G and H are inverses of each other because G + H = I.

Accepted Solution

A:

Answer:Option B.Step-by-step explanation:The given matrices are[tex]G=\begin{bmatrix}7&5\\ \:4&3\end{bmatrix}[/tex][tex]H=\begin{bmatrix}-6&-5\\ \:-4&-2\end{bmatrix}[/tex]Two matrices are inverse of each other if product of both matrices is identity matrix, i.e., [tex]I=\begin{bmatrix}1&0\\ \:0&1\end{bmatrix}[/tex].[tex]\begin{bmatrix}7&5\\ \:4&3\end{bmatrix}\begin{bmatrix}-6&-5\\ \:-4&-2\end{bmatrix}[/tex][tex]\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}[/tex][tex]\begin{bmatrix}-62&-45\\ -36&-26\end{bmatrix}\neq I[/tex]Matrices G and H are not inverses of each other because GH does not equal I.Therefore, the correct option is B.