Let and be invertible square matrices of the same order.

MATHEMATICS · Multi-part · CBSE · Mathematics · Determinants · Determinants

Problem

Let

B

and

C

be invertible square matrices of the same order. (i) Express the inverse of the matrix

D=C^{T}B

in its simplest form in terms of

B^{-1}

and

C^{-1}

only. (ii) For

B=\begin{pmatrix}1&2\\0&1\end{pmatrix},\qquad C=\begin{pmatrix}2&0\\3&1\end{pmatrix},

find

D^{-1}

quickly using the result of part (i) and verify your answer by direct multiplication.