I came across a surprising result.

If A is any matrix of order (mxn) and B is any matrix of order (nxm), such that m>n.

Then determinant of AB is always equal to zero.

Can we prove this?

Hello student,
Please find the answer to your qustion below
Let us take A is 2X1 matrix and B is 1X2 matrix and take some general alphabets to prove this
Let A=and B=[k l]
So AXB=
So |AB|=[ijkl-ijkl]=0

Approved