2 added 174 characters in body
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CJam, 8 bytes

{_z..e>}

Anonymous block (function) that takes the input from the stack and replaces it by the output.

Try it online! Or verify all test cases.

Explanation

{      }    e# Define block
 _          e# Duplicate
  z         e# Zip
   .        e# Apply next operator to the two arrays, item by item
            e# (that is, to rows of the two matrices)
    .       e# Apply next operator to the two arrays, item by item
            e# (that is, to numbers of the two rows)
     e>     e# Maximum of two numbers

CJam, 8 bytes

{_z..e>}

Anonymous block (function) that takes the input from the stack and replaces it by the output.

Try it online!

Explanation

{      }    e# Define block
 _          e# Duplicate
  z         e# Zip
   .        e# Apply next operator to the two arrays, item by item
            e# (that is, to rows of the two matrices)
    .       e# Apply next operator to the two arrays, item by item
            e# (that is, to numbers of the two rows)
     e>     e# Maximum of two numbers

CJam, 8 bytes

{_z..e>}

Anonymous block (function) that takes the input from the stack and replaces it by the output.

Try it online! Or verify all test cases.

Explanation

{      }    e# Define block
 _          e# Duplicate
  z         e# Zip
   .        e# Apply next operator to the two arrays, item by item
            e# (that is, to rows of the two matrices)
    .       e# Apply next operator to the two arrays, item by item
            e# (that is, to numbers of the two rows)
     e>     e# Maximum of two numbers
1
source | link

CJam, 8 bytes

{_z..e>}

Anonymous block (function) that takes the input from the stack and replaces it by the output.

Try it online!

Explanation

{      }    e# Define block
 _          e# Duplicate
  z         e# Zip
   .        e# Apply next operator to the two arrays, item by item
            e# (that is, to rows of the two matrices)
    .       e# Apply next operator to the two arrays, item by item
            e# (that is, to numbers of the two rows)
     e>     e# Maximum of two numbers