Answer:
Step-by-step explanation:
Given two matrices A and B
The product of the matrix A and B is AB
And we know that AB is an "n×n" matrix
We can defined invertible by the rank of the matrix, then, RANK of a matrix is equal to the maximum number of linearly independent columns or rows in the matrix
Also, the rank of an "n×n" matrix is at most "n", an "n×n" having a rank "n" is invertible.
Since, AB is an "n×n" matrix,
AB will be invertible if and only if RANK(AB)=n, and it has a pivots in every rows and columns, so that it ranks will be n,
NOTE: If matrix A is an "n×n"
, if matrix B is an "n×n"
Then, the rank of A cannot be more than "n" and the rank of B cannot be more than "n".
Therefore, Both A and B have rank "n" and they have a pivots in every row and column, so they are both invertible.
