Let A be an m `xx` n matrix. Under which one of the following conditions does `A^(-1)` exist ?

Options

A. m = n only
B. m = n and det A `ne` 0
C. m = n and det A = 0
D. m `ne` n

Answer

B

Explanation

Let a be an m `xx` n matrix, then `A^(-1)` will exist if m = n since only square matrix has determinant and det A `ne` 0
[Since `A^(-1)=(adj A)/(|A|)`]