MCQ
Which of the following is/are correct?
Statement (A): If $A=\left[\begin{array}{rr}3 & 1 \\ -1 & 2\end{array}\right]$, then $A ^2=\left[\begin{array}{rr}8 & -5 \\ 5 & 3\end{array}\right]$
Statement (B): If $A=\left[\begin{array}{rr}3 & 1 \\ -1 & 2\end{array}\right], B=\left[\begin{array}{ll}5 & x \\ 1 & 0\end{array}\right]$ and $A^2=B$, then the value of $x$ is 5 .
Statement (C): For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix.
  • A
    Only A and B are correct
  • Only B and C are correct
  • C
    Only A and C are correct
  • D
    All A, B and C are correct

Answer

Correct option: B.
Only B and C are correct
(b) Only B and C are correct
Explanation:
$\begin{array}{l}A=\left[\begin{array}{rr}3 & 1 \\ -1 & 2\end{array}\right]_{2 \times 2} \\ A^2=\left[\begin{array}{rr}3 & 1 \\ -1 & 2\end{array}\right]_{2 \times 2}\left[\begin{array}{rr}3 & 1 \\ -1 & 2\end{array}\right]_{2 \times 2}=\left[\begin{array}{rr}8 & 5 \\ -5 & 3\end{array}\right]\end{array}$
Statement A is incorrect
$\ldots A ^2= B$
$\left[\begin{array}{rr}8 & 5 \\ -5 & 3\end{array}\right]=\left[\begin{array}{ll}5 & x \\ 1 & 0\end{array}\right]$
x=5
Statement B and C are correct

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