Question

A = \(\begin{bmatrix} 1 &-1 \\ -1 & 1 \end{bmatrix}\) and B = \(\begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix}\) , then AB = 
1. A zero matrix
2. Identity matrix
3. Singular matrix
4. Both 1 and 2
5. None of these

Answer 1

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