Question

If $\mathit{d}\mathit{e}\mathit{t}\mathit{A}\mathbf{=}\mathit{d}\mathit{e}\mathit{t}\mathit{B}$ for two $\mathit{n}\mathbf{\times }\mathit{n}$ matrices A and B, thenAmust be similar to B .

Short answer

Therefore, the A and B are not similar. So, the given statement is not satisfied.

Step-by-step solution

Matrix Definition

Matrix is a set of numbers arranged in rowsand columns so as to form a rectangular array.

The numbers are called the elements, or entries, of the matrix.

If there are m rows and n columns, the matrix is said to be an “m by n” matrix, written “ $m\times n$.”

To check whether the given condition is true or false

For example,

$A=\left[\begin{array}{cc}1& 1\\ 0& 1\end{array}\right],$

localid="1659530638039" $B=l_2$.

Clearly

$detA=detB$

$detA=1$,

but A and B are not similar.

Therefore, the A and B are not similar. So, the given statement is not satisfied.