Answer:
To find the determinant of matrix A, we can use the formula for a 2x2 matrix:
det(A) = (a*d) - (b*c)
In this case, we have:
A = [ -3 8
-8 2 ]
Using the formula, we can calculate the determinant as:
det(A) = (-3 * 2) - (8 * -8)
= -6 - (-64)
= -6 + 64
= 58
Now, to find the inverse of matrix A, we can use the formula:
A^-1 = (1/det(A)) * adj(A)
Where adj(A) is the adjugate of matrix A.
The adjugate of matrix A can be found by swapping the diagonal elements and changing the sign of the off-diagonal elements:
adj(A) = [ 2 -8
8 -3 ]
Now, we can find the inverse of A:
A^-1 = (1/58) * [ 2 -8
8 -3 ]
Multiplying each element by 1/58, we get:
A^-1 = [ 2/58 -8/58
8/58 -3/58 ]
Simplifying the fractions, we have:
A^-1 = [ 1/29 -4/29
4/29 -1/29 ]
Therefore, the inverse of matrix A, A^-1, is:
A^-1 = [ 1/29 -4/29
4/29 -1/29 ]
Explanation: