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?

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- Oct 23rd 2008, 05:50 PMaaronrjInverse and Power Matrices
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? - Oct 23rd 2008, 06:46 PMShyam
First calculate $\displaystyle A^2= A.A $ then find $\displaystyle A^3$ after.

$\displaystyle A^3$ will be $\displaystyle =A^2.A$ - Oct 24th 2008, 04:02 AMHallsofIvy
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.

Quote:

How would I take a^3? Would it be:

-1^3 2^3

1^3 3^3

What would (A^-1)^3 be?