Question

If all the entries of a $\mathbf{7}\mathbf{\times }\mathbf{7}$matrix A are 7, then $\mathit{d}\mathit{e}\mathit{t}\mathit{A}$ must be ${\mathbf{7}}^{\mathbf{7}}$.

Short answer

Therefore, the given condition is not satisfied. So, it is false.

Step-by-step solution

Matrix Definition. 

Matrix is a set of numbers arranged in rows and columns so as to form a rectangulararray.

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.

If all the entries of a $7\times 7$ matrix A are the same, then, we can make the row zero.

Therefore, $detA=0$not, $detA\ne 7^7$.