Find the total number of possible square matrix A of the order 3 with all real entries, whose adjoint matrix B has characterstics polynomial equation as x³ - x² + x +1 = 0

Q. Let

A

be a square matrix of order

3

whose all entries are

1

and let

I_{3}

be the identity matrix of order

3

. Then the matrix

A - 3 I_{3}

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A5×7 matrix has all its entries equal to -1. Then the rank of a matrix is

The correct option is C 1If a m× n matrix has all its entries equal to k ≠ 0, then the rank of the matrix will always be 1. Note: In any non-zero matrix, if all rows or all columns are same, then the rank of that matrix will always be 1.

$A_{5 \times 7}$ matrix has all its entries equal to -1. Then the rank of a matrix is

The correct option is C 1
If a m $\times$ n matrix has all its entries equal to k $\neq$ 0, then the rank of the matrix will always be 1.

Note: In any non-zero matrix, if all rows or all columns are same, then the rank of that matrix will always be 1.