I'm really confused on the topic of multiplicative inverses of matrices. Here's what it said in the book: If A and X are n x n matrices, and AX = XA = 1, then X is the multiplicative inverse of A, written A to the negative power of 1.

But could someone explain to me how it works? There is an "example problem" from the book below.

Question

I'm really confused on the topic of multiplicative inverses of matrices. Here's what it said in the book:  If A and X are n x n matrices, and AX = XA = 1, then X is the multiplicative inverse of A, written A to the negative power of 1.

But could someone explain to me how it works?  There is an "example problem" from the book below.

anonymous · Answer

|dw:1368134648190:dw|

How do I find the inverse of this?