The multiplicative inverse of a matrix is the matrix that gives you the identity matrix when multiplied by the original matrix. ... This tells you that when you multiply a matrix A with its multiplicative inverse, you will get the identity matrix.

How do you know if a matrix has a multiplicative inverse?

Show that the given matrices are multiplicative inverses of each other. Multiply AB A B and BA B A . If both products equal the identity, then the two matrices are inverses of each other.

Which matrix has no multiplicative inverse?

The multiplicative inverse of a square matrix is called its inverse matrix. If a matrix A has an inverse, then A is said to be nonsingular or invertible. A singular matrix does not have an inverse.