Let A = … and M_ij, A_ij respectively denote the minor, co-factor of an element a_ij of matrix A, then which of the following are true? (A) M_22 = -1…

1. Verifying (A): $M_{22} = -1$M22​=−1

To find the minor $M_{22}$M22​, remove the 2nd row and 2nd column from matrix $A$A:
M_{22} = \begin{vmatrix} 1 & 1 \\ 2 & 1 \end{vmatrix} = (1)(1) - (1)(2) = 1 - 2 = -1$ *This statement is **TRUE**.* --- ### **2. Verifying (B): $A_{23} = 0$** To find the cofactor $A_{23}$, first find the minor $M_{23}$ by removing the **2nd row** and **3rd column**:M_{23} = $$\begin{vmatrix} 1 & 2 \\ 2 & 4 \end{vmatrix}$$​12​24​​ = (1)(4) - (2)(2) = 4 - 4 = 0$

Now, apply the cofactor sign rule $A_{23} = (-1)^{2+3} M_{23}$A23​=(−1)2+3M23​:
$$A_{23} = (-1) \times 0 = 0$$A23​=(−1)×0=0
This statement is TRUE.