algebra 2 help? Please?

Question

I need to determine whether the matrices are multiplcative inverse. ( * is used to show separation between each number) for some reason it was running all numbers together.


1 * 2 * -1 , 1 * 0 * 2
-1.5 * -3 * 1.75 , 3 * 2 * -1
0 * -1 * 0.5 , 6 * 4 * 0


Find the inverse of each matrix, if it exists.

-2 1 -1
2 0 4
0 2 5

is there anyone who understands how to do this

Answer 1

For the first one, call the first matrix A and the second one B. You just need to calculate AB and see if it's the 3 x 3 identity matrix, which would be

1 0 0
0 1 0
0 0 1,

and if it is, then the two matrices are multiplicative inverses.

To find the inverse of a square matrix, take one over the determinate of the matrix, and multiply it by the transpose of the cofactor matrix, where the cofactor of each element is the determinate of a matrix constructed by excluding the row and column of that element in the original matrix, and multiplied by -1 if the sum of the row and column is an odd number.