inverse matrices

[SONCEE]

show that the following matrices are inverse of each other.

[1,2 ] [ -3 , 1 ]
[4,6] [2 , 1/2]

 

[galactus]

A two-by-two is easy to find the inverse of:

If \(\displaystyle A=\begin{bmatrix}a&b\\c&d\end{bmatrix}\)

\(\displaystyle A^{-1}=\frac{1}{det(A)}\begin{bmatrix}d&-b\\-c&a\end{bmatrix}\)

 

[pka]

As posted, they are not inverses.
Did you mean \(\displaystyle \left[ {\begin{array}{rr} { - 3} & 1 \\ 2 & { {-} \frac{1}{2}} \\ \end{array} } \right]\)??

 

[SONCEE]

As posted, they are not inverses.
Did you mean \(\displaystyle \left[ {\begin{array}{rr} { - 3} & 1 \\ 2 & { {-} \frac{1}{2}} \\ \end{array} } \right]\)??

yes i did, i'm sorry i wrote it wrong

 

[pka]

If you multiply those two together do you get \(\displaystyle \left[ {\begin{array}{rr} 1 & 0 \\ 0 & 1 \\ \end{array} } \right]\)?

 

[Deleted member 4993]

Use the fact that:

If

\(\displaystyle [A]\cdot \, = \)

then

\(\displaystyle \, = \, [A]^{-1}\)