Correct Answer - Option 1 : A zero matrix
Concept:
A zero matrix or null matrix is a matrix all of whose entries are zero.
An identity matrix is a square matrix having 1s on the main diagonal, and 0s everywhere else.
Calculation:
A = \(\begin{bmatrix} 1 &-1 \\ -1 & 1 \end{bmatrix}\)
B = \(\begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix}\)
AB = \(\begin{bmatrix} 1 &-1 \\ -1 & 1 \end{bmatrix}\)× \(\begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix}\)
AB = \(\begin{bmatrix} 1-1 & 1-1 \\ -1+1 & -1+1 \end{bmatrix}\)
AB = \(\begin{bmatrix} 0& 0 \\ 0 & 0 \end{bmatrix}\), i.e., Zero matrix