Question

If \(\rm A=\begin{bmatrix} 1& 3\\ 5& 2\end{bmatrix}\) and \(\rm B=\begin{bmatrix} 3&2\\ 1& 3\end{bmatrix}\), then |AB| = ?
1. -91
2. -17
3. 84
4. None of these.

Answer 1

Correct Answer - Option 1 : -91

Concept:

Determinant of the product of matrices is equal to the product of determinants of the matrices.

i.e. |AB| = |A| |B|.

 

Calculation:

Given that \(\rm A=\begin{bmatrix} 1& 3\\ 5& 2\end{bmatrix}\) and \(\rm B=\begin{bmatrix} 3&2\\ 1& 3\end{bmatrix}\)

Now, |AB| = |A| |B| = (2 - 15)(9 - 2) = -91.

 

:

The matrix product AB will be \(\rm \begin{bmatrix} 1& 3\\ 5& 2\end{bmatrix}\begin{bmatrix} 3& 2\\ 1& 3\end{bmatrix}\) = \(\begin{bmatrix} 3+3& 2+9\\ 15+2& 10+6\end{bmatrix}\) = \(\begin{bmatrix} 6& 11\\ 17& 16\end{bmatrix}\).

And |AB| = 96 - 187 = -91.