Question

Given, for a matrix
$A=\left[\begin{array}{ccc}5& 3& 5\\ 2& 3& 8\\ 0& 3& 0\end{array}\right],$
what will be its additive identity?

• A. $\left[\begin{array}{ccc}5& 3& 5\\ 2& 3& 8\\ 0& 3& 0\end{array}\right]$
• B. $\left[\begin{array}{ccc}-5& -3& -5\\ -2& -3& -8\\ 0& -3& 0\end{array}\right]$
• C. $\left[\begin{array}{ccc}0& 0& 0\\ 0& 0& 0\\ 0& 0& 0\end{array}\right]$
• D. None of the above

Answer 1

The correct option is C $\left[\begin{array}{ccc}0& 0& 0\\ 0& 0& 0\\ 0& 0& 0\end{array}\right]$

The null matrix or zero matrix is the identity for matrix addition.
$i.e.,\left[\begin{array}{ccc}0& 0& 0\\ 0& 0& 0\\ 0& 0& 0\end{array}\right]$

Or, A + O = O + A = A, where O is the null matrix or zero matrix of same order as that of A.