Question

guyss I hv exam
please help​

Answer 1

AA-1 = A-1A = I

Example: For matrix , its inverse is since

The Inverse of a Matrix

So, what is the inverse of a matrix?

Well, in real numbers, the inverse of any real number a was the number a-1, such that a times a-1 equaled 1. We knew that for a real number, the inverse of the number was the reciprocal of the number, as long as the number wasn't zero.

The inverse of a square matrix A, denoted by A-1, is the matrix so that the product of A and A-1 is the Identity matrix. The identity matrix that results will be the same size as the matrix A. Wow, there's a lot of similarities there between real numbers and matrices. That's good, right - you don't want it to be something completely different.

A(A-1) = I or A-1(A) = I

There are a couple of exceptions, though. First of all, A-1 does not mean 1/A. Remember, "There is no Matrix Division!" Secondly, A-1 does not mean take the reciprocal of every element in the matrix A.