Linear Algebra 11o: There Is Only One Inverse Matrix

[RubberDuckyToy]

4:43 Matrix multiplication is non commutative with 2 notable exceptions:
1.) A or B = Identity
2.) A = B^-1 or B = A^-1
Are those the only exceptions?
What if A and B are diagonal matrices? Wouldn’t two diagonal matrices A and B have the property AB = BA?

[thentust]

Hi, where is your another video explain the reason there is only one inverse matrix??

[namanmishra]

I perform this matrix multiplication on scientific calculater but came an answer different from identity matrix

[sharmaabhi]

Can a non-square matrix say tall matrix, multiply with a say rectangular matrix to give square Identity matrix? And therefore call this latter matrix as inverse of the previous?