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80

If $A$ and $B$ are symmetric matrices of same order, then $A B$ is symmetric if and only if ............. .

Explanation

If $A$ and $B$ are symmetric matrices of same order, then $A B$ is symmetric if and only if $A B=B A$.

$$\begin{aligned} \therefore\quad & (A B)^{\prime} \\ = & B^{\prime} A^{\prime}=B A \\ = & A B \end{aligned} \quad[\because A B=B A]$$

81

In applying one or more row operations while finding $A^{-1}$ by elementary row operations, we obtain all zeroes in one or more, then $A^{-1} \ldots \ldots .$.

Explanation

In applying one or more row operations while finding $A^{-1}$ by elementary row operations, we obtain all zeroes in one or more, then $A^{-1}$ does not exist.

82

A matrix denotes a number.

A
TRUE
B
FALSE
83

Matrices of any order can be added.

A
TRUE
B
FALSE
84

Two matrices are equal, if they have same number of rows and same number of columns.

A
TRUE
B
FALSE