I have a simple 2 x 2 matrix, a =
-1 2
1 3
Correct me if I'm wrong, but the inverse of this matrix is:
1/5 -2/5
-1/5 -3/5
How would I take a^3? Would it be:
-1^3 2^3
1^3 3^3
What would (A^-1)^3 be?
Yes, you are wrong. It should be fairly easy to see that, multiplying the first row of the first matrix by the first column of the second, (-1)(1/5)+ 2(-1/5)= -3/5 when it should be 1. It looks like you have just divided the numbers in the matrix by the determinant. That does NOT give the inverse matrix.
It looks like either you do not know how to multiply matrices or you simply have not thought about multiplying matrices in connection with either of these problems. What is A multiplied by itself?How would I take a^3? Would it be:
-1^3 2^3
1^3 3^3
What would (A^-1)^3 be?