Consider the matrix A= pmatrix 2 & -1 & 3 0 & 4 & 5 1 & 2 & -1 pmatrix

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

Problem

Consider the matrix A=(2−1304512−1).A=\begin{pmatrix}2 & -1 & 3\\ 0 & 4 & 5\\ 1 & 2 & -1\end{pmatrix}. Answer the following: (i) Calculate det⁡(A)\det(A). (ii) On the basis of your answer to part (i), state whether AA is singular or non-singular. (iii) Explain, in not more than three sentences, why the value obtained in part (i) determines the existence or non-existence of A−1A^{-1}.

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