Contrapositive of the statement “If two numbers are not equal, then their squares are not equal.” is :

Which of the following statements is a tautology?

Let $A$ and $B$ be two invertible matrices of order $3 \times 3$. If $\operatorname{det}\left(A B A^{\top}\right)=8$ and $\operatorname{det}\left(A B^{-1}\right)=8$, then $\operatorname{det}\left(B A^{-1} B^{\top}\right)$ is...

The logical statement (MF ST-1) $[\sim(\sim p \vee q) \vee(p \wedge r)] \wedge(\sim q \wedge r)$ is equivalent to

If the system of linear equations $$ \begin{gathered} x-4 y+7 z=g \\ 3 y-5 z=h \\ -2 x+5 y-9 z=k \end{gathered} $$ is consistent, then

If $\mathrm{A}=\left(\begin{array}{ll}2 & 2 \\ 9 & 4\end{array}\right)$ and $\mathrm{I}=\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right)$, then $10 \mathrm{~A}^{-1}$ is equal to

The number of elements in the set $\left\{A=\left(\begin{array}{ll}a & b \\ 0 & d\end{array}\right): a, b, d \in\{-1,0,1\}\right.$ and $\left.(I-A)^3=I-A^3\right\}$ where $I$ is $...

If the system of equations 2x+3y-z=0, x+ky-2z=0 and $2 x-y+z=0$ has a non-trivial solution $(x, y, z)$, then $\frac{x}{y}+\frac{y}{z}+\frac{z}{x}+k$ is equal to :

Let $\alpha$ be a root of the equation $x^2+x+1=0$ and the matrix $...