If $A$ and $B$ are symmetric matrices of same order, then $AB$ is symmetric if and only if

In applying one or more row operations while finding $A^{-1}$ by elementary row operations, we obtain all zeroes in one or more, then $A^{-1}$_____. [exist/ does not exist]

A matrix denotes a number.

Matrices of any order can be added.

Matrices of different order cannot be subtracted.

Matrix addition is associative as well as commutative.

Matrix multiplication is commutative.

A square matrix where every element is unity is called an identity matrix.