Is it possible to contruct a 4x3 matrix b and a 3x4 matrix c such that bc is invertible?

Matrix B has dimensions 4x3 
Matrix C has dimensions 3x4

Write out those dimensions like so: 4x3   3x4
The inner '3's match up so B*C is possible. The dimensions of B*C is 4x4 as these are the outer dimensions when lining up 4x3  3x4

Since B*C is a square matrix, it is possible that an inverse could exist. Keep in mind that this isn't a guarantee as the determinant of B*C could be zero (which would lead to BC being non-invertible). Though of course we'd need more info.

38+105= 143, 39+104=143, and you will find then adding the numbers on opposite sides, moving inwards yields the answer 138 every time. because of this, you’re going to multiply 138 times the number of pairs, which is 34. therefore, 34*138= 4692(i’m sorry if it’s the wrong numbers, but it’s the right concept)