1
KCET 2021
+1
-0

If $$A=\left[\begin{array}{ccc}1 & -2 & 1 \\ 2 & 1 & 3\end{array}\right]$$

$$B=\left[\begin{array}{ll}2 & 1 \\ 3 & 2 \\ 1 & 1\end{array}\right]$$, then $$(A B)^{\prime}$$ is equal to

A
$$\left[\begin{array}{cc}-3 & -2 \\ 10 & 7\end{array}\right]$$
B
$$\left[\begin{array}{cc}-3 & 10 \\ -2 & 7\end{array}\right]$$
C
$$\left[\begin{array}{ll}-3 & 7 \\ 10 & 2\end{array}\right]$$
D
$$\left[\begin{array}{cc}-3 & 7 \\ 10 & -2\end{array}\right]$$
2
KCET 2021
+1
-0

Let $$M$$ be $$2 \times 2$$ symmetric matrix with integer entries, then $$M$$ is invertible if

A
the first column of $$M$$ is the transpose of second row of $$M$$.
B
the second row of $$M$$ is the transpose of first column of $$M$$.
C
$$M$$ is diagonal matrix with non-zero entries in the principal diagonal.
D
The product of entries in the principal diagonal of $$M$$ is the product of entries in the other diagonal.
3
KCET 2021
+1
-0

If $$A$$ and $$B$$ are matrices of order 3 and $$|A|=5,|B|=3$$, then $$|3 A B|$$ is

A
425
B
405
C
565
D
585
4
KCET 2021
+1
-0

If $$A$$ and $$B$$ are invertible matrices then which of the following is not correct?

A
$$\operatorname{adj} A=|A| A^{-1}$$
B
$$\operatorname{det}\left(A^{-1}\right)=[\operatorname{det}(A)]^{-1}$$
C
$$(A B)^{-1}=B^{-1} A^{-1}$$
D
$$(A+B)^{-1}=B^{-1}+A^{-1}$$
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