Question

Prove that a is invertible if and only if determinant of a is not equal to zero

Answer 1

Look, the easy formula to find inverse of a matrix is this formula.

adj(a)/det(a).

Through this formula, we can see that if det(a) is 0, the equation becomes infinity, which sounds nonsensical, as a matrix can never be infinity as a whole.

Through this we can say that matrix a can be invertible if and only if the determinant is non zero.

Hope this helps