Use the technique of Problem 1 to show that if
,
then there does not exist a matrix B such that AB = I. Suggestion: Show that the system of four equations in a, b, c, and d is inconsistent.
Problem 1
Let ,
and
Find B so that AB = I = BA as follows: First equate entries on the two sides of the equation AB = I. Then solve the resulting four equations for a, b, c, and d. Finally verify that BA = I as well.
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