Hello,

Firstly let me tell you a bit about how to calculate rank of a matrix, Rank of a matrix can be calculated by counting the non - zero rows or non - zero coloumns. First we will transform the matrix in to its row echleon form and then count the non-existant zero rows.

And the determinant of the product of two matrices are just the product of two determinant.

I think the answer to this quest must be d, rank of AB <= 3 and det AB will be 0.

Hope this will help you,  kindly check out your answer by recalculating it.

You,  can get more examples regarding the same on internet.

Good Luck!