Which matrices are multiplicative inverses

Explanation : By writing the augmented matrix , and reducing the left side to the identity matrix, we can implement the same operations onto the right side, and we arrive at , with the right side representing the inverse of the original matrix.

Explanation : There are a couple of ways to do this. I will use the determinant method. First we need to find the determinant of this matrix, which is for a matrix in the form:. Substituting in our values we find the determinant to be: Now one formula for finding the inverse of the matrix is. Copyright Notice. View Pre-Calculus Tutors. Anastasiya Certified Tutor. Gardner-Webb University, Doctor of Education Robert Certified Tutor. Reza Certified Tutor. Report an issue with this question If you've found an issue with this question, please let us know.

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Find the Best Tutors Do not fill in this field. Instead, we will augment the original matrix with the identity matrix and use row operations to obtain the inverse. Performing elementary row operations so that the identity matrix appears on the left, we will obtain the inverse matrix on the right. We will find the inverse of this matrix in the next example. Improve this page Learn More. Skip to main content. Module Solve Systems With Matrices. Search for:. Find the Inverse of a Matrix Learning Outcomes Verify that multiplying a matrix by its inverse results in 1.

Use matrix multiplication to find the inverse of a matrix. Find an inverse by augmenting with an identity matrix.

Reciprocal of a Number note: 1 8 can also be written 8 Inverse of a Matrix. When we multiply a matrix by its inverse we get the Identity Matrix which is like "1" for matrices :. The inverse of A is A -1 only when:. So, let us check to see what happens when we multiply the matrix by its inverse:. Because with matrices we don't divide! Seriously, there is no concept of dividing by a matrix.

In that example we were very careful to get the multiplications correct, because with matrices the order of multiplication matters.