CUET Mathematics 2025 29 May Shift 2 PYQs

Let A be a square matrix of order n, then which of the following are TRUE?

(A) $|adj A| = |A|^{n-1}$

(B) $|A. adj A| = |A|^n$

(C) $A. (adj A) = |A|$

(D) $|KA| = K|A|$

(E) $|A^{-1}| = \frac{1}{|A|}, |A| \neq 0$

Choose the correct answer from the options given below:

For a square matrix $A$ of order 3, if $|A| = 2$, then $|adj\ 2A| =$

If $\begin{vmatrix} p-a & 0 & c-r \\ 0 & q-b & c-r \\ a & b & r \end{vmatrix} = 0$ then the value of $\frac{p}{p-a} + \frac{q}{q-b} + \frac{r}{r-c}$ is