Respuesta :
Answer:
(a)First Row, First Column =1
(b)First Row, second Column =0
(c)Second Row, First Column =0
(d)Second Row, second Column =1
Step-by-step explanation:
Given matrix [tex]M=\left(\begin{array}{ccc}-5&3\\-8&5\end{array}\right)[/tex]
The Inverse of a 2X2 matrix
[tex]A=\left(\begin{array}{ccc}a&b\\c&d\end{array}\right)[/tex]
can be found using the following:
[tex]A^{-1}=\dfrac{1}{ad-bc} \left(\begin{array}{ccc}d&-b\\-c&a\end{array}\right)[/tex]
Therefore:
[tex]M^{-1}=\dfrac{1}{(5*-5)-(3*-8)} \left(\begin{array}{ccc}5&-3\\8&-5\end{array}\right)\\=-1\left(\begin{array}{ccc}5&-3\\8&-5\end{array}\right)\\=\left(\begin{array}{ccc}-5&3\\-8&5\end{array}\right)[/tex]
Next, we find the product [tex]M^{-1}M[/tex]
[tex]M^{-1}M=\left(\begin{array}{ccc}-5&3\\-8&5\end{array}\right)\left(\begin{array}{ccc}-5&3\\-8&5\end{array}\right)\\=\left(\begin{array}{ccc}-5*-5+3*-8&-5*3+3*5\\-8*-5+5*-8&-8*3+5*5\end{array}\right)\\=\left(\begin{array}{ccc}1&0\\0&1\end{array}\right)[/tex]
Therefore:
(a)First Row, First Column =1
(b)First Row, second Column =0
(c)Second Row, First Column =0
(d)Second Row, second Column =1
NOTE: The multiplication of a matrix and its inverse always gives the identity matrix as seen above,
