Find the multiplicative inverse of the matrix, if it exists.

Question

Find the multiplicative inverse of the matrix, if it exists.

 

A =  −5 5
         6 4

Answer 1

det   A = -20 - 30 = -50. Therefore (since determinant is not zero) A^-1 exists.

 

The inverse of a 2 by 2 matrix is formed by these two steps:

1.  divide upper left & lower right elements of the matrix by the determinant value; then interchange their positions.

2.  change signs of the other two elements of the matrix, then divide them by the determinant value.