Test Index

UPSC NDA Math Model Paper 4

© examsnet.com

Question : 65 of 120

Marks: +1, -0

If

A = \begin{bmatrix} 0 & -i \\ i & 0 \end{bmatrix}

B = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}

are matrices, then

AB + BA

is:

a diagonal matrix
an invertible matrix
a unit matrix
a null matrix

Solution:

Given:

A = \begin{bmatrix} 0 & -i \\ i & 0 \end{bmatrix}

and

B = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}

AB = \begin{bmatrix} 0 & -i \\ i & 0 \end{bmatrix} \times \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}

= \begin{bmatrix} 0+0 & i+0 \\ 0+i & 0+0 \end{bmatrix} = \begin{bmatrix} 0 & i \\ i & 0 \end{bmatrix}

And

BA = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} \times \begin{bmatrix} 0 & -i \\ i & 0 \end{bmatrix}

= \begin{bmatrix} 0+0 & -i+0 \\ 0-i & 0+0 \end{bmatrix} = \begin{bmatrix} 0 & -i \\ -i & 0 \end{bmatrix}

\therefore AB + BA = \begin{bmatrix} 0 & i \\ i & 0 \end{bmatrix} + \begin{bmatrix} 0 & -i \\ -i & 0 \end{bmatrix}

= \begin{bmatrix} 0+0 & i-i \\ i-i & 0+0 \end{bmatrix} = \begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}

© examsnet.com

Go to Question:

Prev Question

Next Question