The Number of all Possible Matrices of Order 3 × 3 with Each Entry 0 to 1 is

Number of Possible Matrices of Order 3 × 3 with Each Entry 0 to 1

The total number of elements in a 3 × 3 matrix is 9 as 3 elements will be there in each row and 3 elements in each column. Now each element in the 3 × 3 matrix can be selected in two ways i.e. it can be either 0 or 1. Therefore all the 9 elements can be chosen in 29 ways which will be equal to 512. Hence, the required number of matrices is 512 which is the correct answer.

Different Types of Matrices

There are different types of matrices such as:

• Row Matrix
• Column Matrix
• Square Matrix
• Rectangular Matrix
• Diagonal matrix
• Scalar Matrix
• Zero or Null Matrix
• Unit or Identity Matrix
• Upper Triangular Matrix
• Lower Triangular Matrix

Summary:

The Number of all Possible Matrices of Order 3 × 3 with Each Entry 0 to 1 is

512 is the total number of possible matrices of order 3 × 3 with each entry 0 to 1. It can be determined by using the multiplication principle. There will be 9 elements in the matrices of order 3 × 3 wherein the 9 elements can be chosen in 29 ways which will be equal to 512.

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