Matrix Inverse Problem: Troubleshooting Proof and Multiplication Error

[DethRose]

im doing a matrix inverse problem and have the inverse but when i do the proof the book says it should look like this:

2 -3 -5/2 -3/2 equals 1 0
-4 5 times -2 -1 0 1

but if you muliply those shouldn't you get -10/2 + 6 which doesn't equal 1

help please

 

[assyrian_77]

What do you mean by those numbers? Do you mean this:

$$\left(\begin{array}{cc}2&-3\\-4&5\end{array}\right)\times\left(\begin{array}{cc}-5/2&-3/2\\-2&-1\end{array}\right)$$

If so, that does indeed give you the identity matrix. Check your calculation again.

 

[VietDao29]

im doing a matrix inverse problem and have the inverse but when i do the proof the book says it should look like this:

2 -3 -5/2 -3/2 equals 1 0
-4 5 times -2 -1 0 1

but if you muliply those shouldn't you get -10/2 + 6 which doesn't equal 1

help please

As a matter of fact, it does:
$$\left( \begin{array}{cc} 2 & -3 \\ -4 & 5 \end{array} \right) \times \left( \begin{array}{cc} -\frac{5}{2} & -\frac{3}{2} \\ -2 & -1 \end{array} \right) = \left( \begin{array}{cc} 2 \times \left( -\frac{5}{2} \right) + (-3) \times (-2) & 2 \times \left( -\frac{3}{2} \right) + (-3) \times (-1) \\ -4 \times \left( -\frac{5}{2} \right) + 5 \times (-2) & -4 \times \left( -\frac{3}{2} \right) + 5 \times (-1) \end{array} \right) = \left( \begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array} \right)$$, the desired result. :)

 

[0rthodontist]

but if you muliply those shouldn't you get -10/2 + 6 which doesn't equal 1

-10/2 + 6 = -5 + 6 = 6 - 5 = ?