Question

If A=\(\begin{bmatrix}i&1\\0&i\end{bmatrix}\), then the correct relation is ___________

(a) A+A’=\(\begin{bmatrix}1&0\\-1&0\end{bmatrix}\)

(b) A-A’=\(\begin{bmatrix}1&0\\-1&0\end{bmatrix}\)

(c) A+A’=\(\begin{bmatrix}0&1\\-1&0\end{bmatrix}\)

(d) A-A’=\(\begin{bmatrix}0&1\\-1&0\end{bmatrix}\)

I had been asked this question in an interview for job.

The doubt is from Transpose of a Matrix topic in section Matrices of Mathematics – Class 12

Answer 1

Right option is (d) A-A’=\(\begin{bmatrix}0&1\\-1&0\end{bmatrix}\)

The best I can explain: Given that, A=\(\begin{bmatrix}i&1\\0&i\end{bmatrix}\)

⇒A’=\(\begin{bmatrix}i&0\\1&i\end{bmatrix}\)

∴A-A’=\(\begin{bmatrix}i&1\\0&i\end{bmatrix}\)–\(\begin{bmatrix}i&0\\1&i\end{bmatrix}\)=\(\begin{bmatrix}i-i&1-0\\0-1&i-i\end{bmatrix}\)=\(\begin{bmatrix}0&1\\-1&0\end{bmatrix}\).