I am trying to find the inverse of matrix A but I don't know how to do it with sin and cos. Please help.

Question

A=6e3tsin(6t) −6e4tcos(6t)
−5e3tcos(6t) −5e4tsin(6t)


then A−1=

Answer 1

The inverse of a 2x2 can be done as follows:

For matrix, A=
|a b|
|c d|
The inverse A^-1=
|d -b|
|-c a| / (ad-bc)

For example:
If A=
|4 5|
|6 7|
A^-1 =
|7 -5|
|-6 4| / (28-30)
=
|-3.5 2.5|
|3 -2|

Check:
|4 5| |-3.5 2.5|
|6 7| |3 -2|
=
|1 0|
|0 1|