Let , where . If , then the number of such matrices is: Note: denotes the adjoint of…

MATHEMATICS · Single correct · CBSE · Mathematics · Determinants · Determinants

Problem

Let

A=\begin{bmatrix}x&y&-z\\1&2&3\\1&1&2\end{bmatrix}

, where

x,y,z\in\mathbb{N}

. If

\det(\operatorname{adj}(\operatorname{adj} A))=2^8\cdot3^4

, then the number of such matrices

A

is: Note:

\operatorname{adj} A

denotes the adjoint of the square matrix

A

. (a) 220 (b) 45 (c) 55 (d) 110