If A= 3 & 4 2 & 4 ,B= -2 & -2 0 & -1 then (A+B)^ -1 = - Vidyadip

MCQ

If $\text{A}=\begin{bmatrix} 3 & 4 \\ 2 & 4 \end{bmatrix},\text{B}=\begin{bmatrix} -2 & -2 \\ 0 & -1 \end{bmatrix}$ then $(A+B)^{-1}=$

A
Is $A$ akew$-$symmetric matrix.
B
$A^{-1}+B^{-1}$
C
Does not exist.
✓
None of these.

✓

Answer

Correct option: D.

None of these.

We have
$(\text{A}+\text{B})=\begin{bmatrix} 1 & 2 \\ 2 & 3 \end{bmatrix}$
$\therefore|\text{A}+\text{B}| = -1\neq0$
Thus, $(A+B)^{-1}$ exists.
Now,
$(\text{A}+\text{B})^\text{T}=\begin{bmatrix} 1 & 2 \\ 2 & 3 \end{bmatrix}$
Here,
$(\text{A}+\text{B})^\text{T}\neq-(\text{A}+\text{B})$
Hence, it is not a akew symmetric matrix.
We also know that $A^{-1}+B^{-1}$ is not the same as $(A+B)^{-1}$.

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