Answer
$B^2$ is a defined expression, and the resultin matrix is:
$B^2 =| 1 \space \space -2| $
$ \hphantom {B^2 =.} | 0 \hphantom {--.}1| $
Work Step by Step
1. Check if the expression is defined.
$B^2$ is the same as $BB$, which is a multiplication.
For a matrix multiplication, the length of the row in the first matrix must be equal to the length of the column in the second one.
Length of the row in A: 2
Length of the column in A: 2
Therefore, this expression is defined.
2. Evaluate it:
$(B^2)_{11} = (B_{11} \times B_{11} + B_{12} \times B_{21})$
$(B^2)_{12} = (B_{11} \times B_{12} + B_{12} \times B_{22})$
$(B^2)_{21} = (B_{21} \times B_{11} + B_{22} \times B_{21})$
$(B^2)_{22} = (B_{21} \times B_{12} + B_{22} \times B_{22})$
$(B^2)_{11} = 1 \times 1 + (-1) \times 0 = 1$
$(B^2)_{12} = 1 \times (-1) + (-1) \times 1 = -2$
$(B^2)_{21} = 0 \times 1 + 1 \times 0 = 0$
$(B^2)_{22} = 0 \times (-1) + 1 \times 1 = 1$
$B^2 =| 1 \space \space -2| $
$ \hphantom {B^2 =.} | 0 \hphantom {--.}1| $
